The word 同い年 is presumably related to the adjective 同じ. But what happened to the consonant in the root? I thought this might be an example of イ音便, but typically this happens to -k, -g only.
Is this odd change idiosyncratic to this word? Or does 同じ decompose further into ona-j-i such that there is some other root ona-?
I had a look at the 日本国語大辞典【にほんこくごだいじてん】 (NKD) entry. The NKD is a bit like the Oxford English, it's one of the better dictionaries for giving word derivations.
According to the entry, this reading onaidoshi is an irregular sound shift from older onajitoshi. The onaidoshi version first shows up in 1563.
Phonologically, it looks like the voicing on the じ influenced the と to voice to ど. And with the じ and the ど both starting with front-of-the-mouth consonants, I can see how the consonant in じ would elide (become omitted).
→ At any rate, consider this particular word as a kind of one-off: memorize it, but don't view this as indicative of any common pattern where ～じ becomes ～い.
