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 Thomas Cleary B 1825 +/- 1 yr, somewhere in Ireland, with the father's forename unknown, I found 6 rcds, with 1 in 1825 (exact), Co. Limerick, St. John's RC parish. For this rcd, the father's forename was James.
For Ellen Cleary B 1837 +/- 3 yrs, Co. Dublin, ditto, I found 2 rcds in 1835, both in Kingstown RC parish. Father's forenames were James and David.
For Thomas Quigley B 1831 +/- 3 yr, Co. Tipperary, with the father's forename unknown, I found 3 rcds: 1831 St. Mary's (Clonmel), 1832 Youghalarra, and 1833 Youghalarra RC parishes. Father's forenames were all John.
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.