"Hirable" or "hireable"

Apparently the rule for attaching suffixes is as follows:

If suffix begins with a vowel (a,e,i,o,u,y)
Root will attach directly to it
If suffix begins with a consonant
Root will need a combining vowel before attaching to the suffix

As in Example word: cardiogram
Breakdown of word: cardi/o/gram
Root = cardi
Combining vowel = o
Suffix = gram
Note: Suffix begins with a consonant
Combining vowel is needed

While Example word: cardialgia
Breakdown of word: cardi/algia
Root = cardi
Suffix = algia
Note: Suffix begins with a vowel
Combining vowel is not needed

However, there are words that do not follow this rule: i.e. "Friend-ship", "Govern-ment"

So I would redefine the rule a bit, as it isn't actually mine's.

If suffix begins with a vowel , and the root word ends with a vowel or consonant, the suffix attaches directly.

If however, the suffix begins with a consonant, and the root word ends with a vowel, it will need a combining vowel. If however, the root word ends with a consonant, the suffix will attach with no combining vowel.

Which means your example would be written "hireable"

This is starting to become a bit of a hoary old chestnut. Since OP has already established that both forms are and have been in widespread use for some time, what does it mean to ask "which is correct"?

In this particular case, although the NGram doesn't really make it clear, hirable really is becoming increasingly common. So by one standard, that's the spelling of the future, and is therefore arguably 'more correct'.

On the other hand, hireable was clearly the more prevalent form in the past - certainly in various linguistic subsets (in fact, it's still the preferred British usage, though that is changing even as I write). So arguably few people would seriously criticise anyone for using a more 'traditional' form.

In short, I think this question steers dangerously close to breaching FAQ guidelines which specify that questions should preferably admit of a single clear-cut answer which most competent speakers can agree on.

Languages evolve, Americans spell and pronounce words differently to British. To me hireable looks less likely to have the word mispronounced. Hireable without an e looks problematic as without the e after the first r the I sound has several options. Possibly a short I sound ?

This question was asked and answered about 10 years ago, although no answer was at that time accepted and usage was arguably in flux.

Today, an updated Ngram shows that hirable was been the clear preference for the past 20 years, and has been preferred most of the time since the 1940s aside from a brief interlude.

I think we can confidently declare hirable to be the preferred spelling at this time and for the foreseeable future.