I've developed a data pack that allows Riptide, Channeling, and Loyalty to be combined together. Anvils will work to combine Riptide but only when you are not in rain and Riptide is applied first; enchantment tables won't apply them together though.

The data pack is downloadable here.

Concepts used

• I used commands from Bruno Rodrigues's answer to detect the weather. If you look at the function files, the commands will summon an armour stand at (0, 255, 0) and check the weather using it.

  summon armor_stand ~ ~ ~ {Invulnerable:1b,Invisible:1b,Fire:32766s,CustomName:'"rain"'}
  

  execute as @e[limit=1,name=rain,nbt={Fire:0s}] at @s run scoreboard players set $rain trident_inRain 3
  execute as @e[limit=1,name=rain,nbt={Fire:0s}] at @s run data modify entity @s Fire set value 30000
  execute as @e[name=rain] if score $rain trident_inRain matches 1.. run scoreboard players remove $rain trident_inRain 1
  

• I used another answer from Bruno Rodrigues to check if the player is exposed to rain. This technique involves checking to see if all blocks above you are air. I set commands to cut a hole at column (0, 0), and then tested for players with that:

  fill 0 2 0 0 255 0 minecraft:air
  

  execute as @a at @s if blocks ~ ~1 ~ ~ 255 ~ 0 2 0 all run ...
  

• I used a technique that displays fake CanPlaceOn/CanDestroy data on items through the item's lore, and modified it to display fake enchantments instead. When a user is not in the rain, the Riptide enchantment is removed from the enchantments list and a fake Riptide enchantment is added via the lore.
• I used player inventory modification in order to modify player inventory data. This involves a special loot table, downloadable here.

  loot replace entity @p hotbar.0 1 mine 0 0 0 stick{drop_contents:1b}
  

If you experience any problems with this data pack, please create an issue on GitHub instead of commenting below!