Hope your wife (if she isn't Irish herself) can get a certified copy of photo ID of her parent/grandparent (if she's following that route, that is).
My daughter is doing the same, based on her 94 year old grandmother's Irish birth. We're struggling a bit on that because the gran, my Mum, has no official photo ID, not even a bus pass, and the Consulate's position is "no document - no passport" .