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 McAuliffe B 1838 +/- 4 yrs, Co. Cork, with a father forenamed Pat(rick), I found 2 rcds: 1835 and 1838. The parishes were Milford and Newmarket respectively. A view of the B rcds SHOULD reveal John's parents names. This will validate/invalidate the rcds.
For Pat(rick) McAuliffe M 1834 +/- 4 yrs, Co. Cork, I found 14 rcds - too many to easily summarize here; however, two (1831 and 1835) are in Kanturk parish.
If you are able to validate the above rcds, you have a small chance of discovering one more earlier generation.
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.