I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Unless the county is known, there is AT LEAST a 35% chance the ancestor's rcds aren't in the database.
For Nancy Mooney B ????, I found 2 B rcds in 1833 Antrim. However, neither had Andrew listed as a father.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.