Since Mary Margaret Gavin was born in the US, if her father John was born in Ireland he must have emigrated.
Do you have his date of birth and parents names from his and his children's US records? Was he born in County Mayo or Ireland? His US Naturalisation records may help identify his birthplace in Ireland or County Mayo. There's a list of the names of all the towns and townlands in County Mayo and Ireland at http://www.seanruad.com
and pick Mayo or any county in Ireland as your search county.
If he was born after 1864 and his birth was registered in Irish civil registrations records (many weren't), there may be an Irish civil birth record for him.