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 Fagan B 1815 +/- 4 yrs somewhere in Ireland with the father's forename unknown, I found 39 rcds - too many to summarize here.
For John Fagan M 1840 +/- 4 yrs somewhere in Ireland, I found 31 rcds - again, too many.
For Ann Cowan M ditto, I found 4 rcds: 1838 Westmeath, 1842 Dublin, 1843 Limerick, and 1843 Kildare. A comparison with those for John revealed no potential matches. Their rcds may be among those yet to be transcribed. Suggest you wait until they are. This may take time; be patient.
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.