I had a look at the (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 influenced the to voice to . And with the and the both starting with front-of-the-mouth consonants, I can see how the consonant in 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 becomes .