There is not just one form of Rogue. I can see at least these variants:

• combat rogue (focused and getting and using advantage)
• charisma rogue, focused on social skills. Not all of them excel in combat
• DNDBeyond lists at least 9 different Archetypes. While you only select those at level 3, you are already working/playing with them at level 1.

If you do not got a combat rogue, you do not really need to worry that much.

Reliable ways to get advantage:

Druids belong to the comparatively sturdy/rarely combat casting Divine Spellcasters. Unlike the average Arcane caster, they can stand in front. And Druids are even better at it, thanks to Animal Form (at level 2). So even without spells, the Druid can easily help give advantage by flanking.

If you think you need extra characters, how about a Dog? Or trained Wolf? Not a animal companion but just a plain old trained animal. Wolves are still really good with tripping enemies in 5E and have stealth, but prone is less useful (attacker disadvantage for prone, no mentioned advantage for melee attackers). While the 5E Dog, has Bark to frighten enemies (which grants advantage to everyone else). And as they are not scaling up from CR <1 like a Animal Companion or Familiar would, so it would be no issues for balance. Might even become mascot.

But it might not really be the problem you imagine it:

At level 1, the enemy hitpoints and skills are not that big either. One time sneak attack damage from stealth could down or almost finish a enemy. If they need repeated sneak attacks over multiple rounds to down a enemy at level 1, chances are you went wrong with encounter design way before this Advantage consideration

And level 2 where the issues become less relevant is not far off.

Give your rogue a horse

The rogue can ride up (from a great distance away, thanks to the horse's speed) and Sneak Attack an enemy, thanks to the (obviously) adjacent horse. A riding horse has terrible AC, but has comparable hitpoints to your 1st-level PCs. A warhorse would be sturdier - even more so with barding.

Advanced tactics

There is some disagreement on whether you can interleave your actions and your mount's actions. (This disagreement is further complicated by the fact that Jeremy Crawford's tweets are no longer considered official rules, merely rulings.) Here are two strategies your rogue can employ, depending on your ruling.

Ready, hit, run

This is definitely allowed by the rules, but means that the dual-wielding rogue will only get one attack.

1. The rogue uses the Ready action, set to trigger when she is in range. The rogue ends her turn.
2. The mount's turn begins. The rogue instructs the mount to move up to an enemy.
3. Once in range, the rogue's readied attack triggers, dealing Sneak Attack thanks to the adjacent mount.
4. The rogue instructs the mount to Disengage, and then move away. The rogue cannot be targeted by an opportunity attack, because she is not using her own movement to leave the enemy's reach.

Run, hit, run

This has been allowed at every table I've played at, but depends on how you read the mounted combat rules. I would recommend ruling this way to allow the dual-wielding rogue to use both attacks.

1. The rogue instructs the mount to move up to an enemy.
2. Once in range, the rogue attacks the enemy, dealing Sneak Attack thanks to the adjacent mount. (No need to use Ready with this ruling.)
3. The rogue instructs the mount to Disengage, and then move away. Again, the rogue cannot be targeted by an opportunity attack.

Encourage your rogue to go Swashbuckler at level 3

If the horse is your rogue's main source of Sneak Attack, then some enemy mage is going to cast fireball eventually, and she's going to have a bad time. The Swashbuckler subclass is practically made for melee dual-wielding rogues, thanks to Rakish Audacity (XGtE, p. 47):

Rakish Audacity

[...]

You also gain an additional way to use your Sneak Attack; you don't need advantage on the attack roll to use your Sneak Attack against a creature if you are within 5 feet of it, no other creatures are within 5 feet of you, and you don't have disadvantage on the attack roll. All the other rules for Sneak Attack still apply for you.

Have your rogue consider the Mounted Combatant feat

If your rogue enjoys mounted combat, then the Mounted Combatant feat is a nice upgrade. First, it provides offensive improvements:

• You have advantage on melee attack rolls against any unmounted creature that is smaller than your mount.

Many common mounts are Large creatures, so your rogue will have advantage against anything Medium or smaller. Given that most humanoids are Medium, this is a significant benefit.

The feat also provides major defensive benefits to your rogue's mount:

• You can force an attack targeted at your mount to target you instead.
• If your mount is subjected to an effect that allows it to make a Dexterity saving throw to take only half damage, it instead takes no damage if it succeeds on the saving throw, and only half damage if it fails.

No longer does your rogue have to worry about a stray fireball taking out her horse in one shot. After a level or two, your rogue will be tankier than her horse, so it makes sense to redirect attacks away from it.

Optimally, your rogue would be a variant human, in order to take Mounted Combatant at level 1, but picking it up later works fine, too.

I think you might be worrying too much, as long as the Adventure is level appropriate, and you adapt the challenge ratings of the encounters to match the party, they will learn their characters and find a way.

The Druid picking circle of the moon at level 2 can be a good tank, if you reduce things too much they will get the wrong information on which to base their decisions.

I'm not saying the druid has to pick this to make it work, there are many ways for them to progress, just give them a real adventure and let them succeed or fail.

My 10 year old daughter is playing a second level druid and is halfway through The Sunless Citadel (Tale from the Yawning Portal) on her own and so far, I haven't reduced any of the encounters.

Let them play for real

When I started with AD&D in the early 80-ies, one of the first things they mentioned in DMG, was that as a DM you can do pretty much whatever you want. There are no rules you can't change, remove or bend to your liking.

The whole point of RPG is for the players to have an adventure and being part of a story. The "rules" are there just to get you going in the right direction and to make sure things are somewhat balanced, reasonable and realistic.

So, the best you can do is to just put the books aside and focus on the story and the adventure.

Disregard what level the PC are, and instead think about them, their background, their goal and ambitions and also consider what the players are like....what do they like and so on.
The fighting should be a small part of the game session, and it should flow and go fast. Instead of focusing on stats, skills, proficiencies and other technical details, just tell the players what equipment they have, what their clothing is like, what weapons they carry and if they are any good at using them or if they are beginners and have just learned the basics.

Then when the PC wants to do something just tell them how difficult that action is going to be for them. For example, if they want to climb a 7' wooden fence, then tell the rogue that he think he would not even need to slow down to get over it, while you tell the druid that he think he will probably need some help or find something he can stand on.

Make it clear to them that they are not fighters, so they need to carefully pick their fights and make sure they happen by their choice.

So stop worrying about sneak attacks and whatever, focus on the story and the adventure, and make sure that there are other ways than fighting to solve problems and finish the adventure.

For Druid + Rogue at level 1; combat is not necessarily required.

Focusing on the rogue's DPR is, IMO, you as DM viewing this party through a very narrow lens. I suggest that, since (1) you only have two players, and (2) neither of them is from a warrior archetype, the adventures that you run for them until they get to second level should focus more on role play, exploration, and evasion / mobility and a bit less on melee combat. But when they do opt for melee combat, they need to try and engage on their own terms. (Credit: Sun Tzu's theory)

Why?

In-world, in a narrative sense, the odds that a Rogue and a Druid go and mix it up in the dark halls of a dungeon underground aren't very high. And, by crafting the adventures as suggested you get them working as a team from the get go.
Beyond that, they may not need a tank to create advantage.

How can the Druid help the Rogue get advantage?

Occasionally, with the Help action, but does the Druid player buy into that? Maybe and maybe not, but in any case that is between the two players to figure out. They need to work as a team because there are only two of them.

In some situations, Help will be a good use of an action, in others it will not. Let them figure that out by playing and by making decisions / choices.

Some Druid spells can offer advantage. Again, it is your players who need to work as a team to make the most of this.

1. Entangle (SRD p. 140)
   Note that a creature that fails their save is

   ... restrained by the entangling plants until the spell ends.

   From Appendix A, conditions, Restrained

   Attack rolls against the creature have advantage, and the creature’s attack rolls have disadvantage.

   Rogue attack with advantage enables sneak attack.

2. Faerie Fire (SRD p. 141)

   Any attack roll against an affected creature or object has advantage if the attacker can see it, and the affected cre ture or object can’t benefit from being invisible.

   Rogue has advantage, Sneak attack.

From your comment:

My players have little experience overall and none with D&D 5e. It is their wish to start at level 1 in order to keep things simple.

It is OK to coach your players if they are new; you are the DM, coaching is a part of your role.

Change your DM'ing paradigm to fit your two-player party

Their first level of adventuring needs to empasize using their wits, not brawn, to accomplish their goals. Between the Druid's spells and the Rogue's ability to succeed on ability checks, and to Stealth around, and to occasionally apply a Sneak Attack if someone gets up into the Druid's grill, you can have some exciting and challenging adventures without a tank.

At level 2 Rogue gets cunning action, Druid gets wild shape; their options expand significantly.

Experience:
Two of us played a two-rogue party for a session (urban setting) to help a DM get used to running a game. We used ranged attacks, movement, and anything but melee combat to achieve our aims. It's doable, it's fun, and it's still dangerous to the PC.

You don't.

The choice of class is one of the few things the player has control of, and picking poorly is as valid as picking well.

As a DM it is your job to be fair, and making accommodations for one player is unfair to the other player (s) unless you make equal accomodations for them.

Eventually the rogue will shine, but let the player figure out how.

Taking this to an RP level, why would their character run into melee when it isn't the best choice? If they can't explain why they do it, then maybe they shouldn't if they are attempting to play a character with self preservation.

Equally, a suicide rogue is going to end up shoehorning the druid into a healer role which would frustrate me if I was that druid. Maybe if a rogue doesn't work then they shouldn't be a rogue.

Either way, don't let this player have their cake and eat it too.

Avenues of Sneak Attack

• Ally adjacent to the enemy
• Having advantage on attack roll

Provide an front line NPC.

Your concern about NPCs doing the heavy lifting is well founded. I suggest taking a page out of the Ars Magica books and providing them with a "shield grog" or two. Essentially, an NPC that does little but provide a front line for the interesting characters of your players to do the actual work. If you want to be on the nose about it, literally equip them with two shields and give them no attack actions.

This can add complication to the encounters as they player characters might have to devise ways of keeping these shield grog NPCs alive and happy. You can get into making these NPCs non-throw away in many different ways, but that is entirely a different question.

Provide ample means for attack with advantage.

The primary way many rogues get attacks with advantage is by attacking from concealment. Essentially, hide, shoot, hide.

Design terrain and encounters to facilitate hiding

Dark hiding places and corners around which they can use their cunning action to hide after attacking are welcome additions to encounter maps for rogues. Interesting layouts can provide a clever rogue with opportunities to move around corners, duck out of sight, and generally be a difficult to track scamp.

Consumable items providing hiding or invisiblity

Consumable or rechargeable invisibility items or items that provide hiding are a more straight forward dues ex machina way of giving a rogue a method of gaining attacks with advantage.

These require less clever encounter designs, but does need to have a more balanced adventure design where the limited resource is strained between utility opportunities and combat. That topic is another question entirely.

Experiment!

Have criteria for what you define as working, e.g. "When the rogue had opportunity to use sneak attack in more than 50% of their turns". Then try different methods and see if they work according to what you think working should be.

Solicit the opinions of your players. Specifically ask if they found what was tried fun or interesting.