I research the Irish Family History Foundation's database. It contains 12,700,000 surviving rcds for abt 70% 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 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 John McAuliffe B 1849 +/- 4 yrs somewhere in Ireland with a father forenamed Jer(emiah), I found 5 rcds: 2-1847 Cork, and 3-1851 Cork.
For Jer(emiah) McAuliff M 1845 +/- 4 yrs somewhere in Ireland, I found 7 rcds: 1842 Limerick, 3-1843 Cork, and 3-1845 Cork. The one, if any, which shows Cat(herine) as the bride's name is likely for your ancestor.
For Jer(emiah) McAuliff B 1825 +/- 4 yrs somewhere in Ireland with the father's forename unknown, I found 1 rcd in 1824, Co. Cork, Donoughmore RC parish. Father's forename was Denis.
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.