I research the Irish Family History Foundation's database. It contains 12,800,000 surviving rcds for abt 70% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Cos. Donegal and Derry were recently added to the database.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 30%.
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 Pat(rick) Killeen B 1879 +/- 4 yrs, Co. Mayo, with the father's forename unknown, I found 26 rcds - too many to summarize here. Seven have father's forenamed John.
For John ditto, there are 17 rcds. Three have father's forenamed John.
For Edward ditto, I found 2 rcds: 1881, 1-civil (Kilkelly CP), and 1-church (Aghamower RC parish). Father's forenames were John in both cases. These are likely duplicates.
Aghamore seems to be the parish common to all 3 names. John seems to be the common father's forename. Experiment a bit to make sure there are no other commonalities.
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.