I search 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 parish, 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).
Myles is a RARE forename. This means there are few false positives. For Myles O'Reilly B 1818 +/- 4 yrs, I found 1 B rcd in 1815 Cavan.
For Julia O'Reilly B 1827 +/- 4 yrs, I found 5 B rcds: 1825 Cork, 1827 Dublin, 1827 Cork, 1829 Meath, and 1830 Cork. None were in Cavan. Meath abuts Cavan. The 1829 Meath rcd seems the most likely candidate.
For Pat(rick) Sullivan B 1829 (exact) in all Ireland, I found 22 B rcds with 10 in Cork. Co. Kerry rcds aren't in the database yet. Since he sailed from Limerick southwest Cork or Kerry are likely counties. Without a parent name, placename, exact DOB, etc, it isn't possible to separate the correct rcd, if any, from the false possitives.
Since Co. Kerry and some of Cork rcds aren't in the database, I suggest you wait until they are. Meanwhile comb RC parishes registers for their marriage rcds. These SHOULD show their parents' names and sometimes their origins.
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.