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).
Note 4 - Microfilms of parish church rcds are kept by the National Library of Ireland.
For Mary Foley B 1857 (exact), Newcastle West, Co. Limerick, with a father forenamed John, I found 1 rcd.
For John Foley M 1841 (exact), Newcastle West, Co. Limerick, I found 1 rcd.
For Elizabeth Davis M ditto, I found ditto. These are HIGHLY likely to be for these ancestors. A view of the M rcds MAY show their parents' names as well as other info. This info will be useful in validating earlier B/M rcds.
For Elizabeth Davis B 1820 +/- 4 yrs, Co. Limerick, I found 0 rcds. Newcastle West parish rcds begin in 1815. But, there is no guarantee that all events were rcd'd, or all rcds survived.
For John Foley B 1818 +/- 4 yrs, Co. Limerick, I found 7 rcds: 1814, 2-1815, 2-1817, 1818, and 1820.
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.