I research 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.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For John Fahey B 1870 (exact), Bullaun CP, or Bullaun RC parish, Co. Galway, I found 0 rcds.
For John Fahey B 1879 (exact), Loughrea RC, or Loughrea CP, ditto, I found 0 rcds.
For John Fahey B ditto, in other Galway east parishes, I found 8 rcds. Only the fore and sur names are on the rcds. You would have to roll the dice on the 8 rcds and hope that one shows the Mar 25, 1870 DOB.
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.