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 a Patrick Cleary and Mary Maddigan M 1853 +/- 4 yrs, I can't find matching M rcds in Co. Limerick.
For Mary Maddigan B 1834 +/- 2 yrs, somewhere in Ireland, with a father forenamed Thomas, I found 1 rcd, 1833, Kilcornan & Stonehall RC parish. A view of the detailed rcd SHOULD show her parents' names as well as other info. This is useful in identifying and validating B/M rcds for earlier generations.
For Thomas Maddigan M 1829 +/- 4 yrs, Co Limerick, I found 5 rcds: 1830 Kilcornan & Stonehall, 1832 Kilcornan & Stonehall, 1832 Kilcornan & Stonehall, 1833 St. Michael's, and 1833 Askeaton RC parishes. One of these MAY show the parent's names revealed above.
For Pat(rick) Cleary B 1820 +/- 4 yrs, Co. Limerick, with the father's forename unknown, I found 11 rcds: 1817, 2-1818, 2-1819, 1820, 1821, 2-1823, and 2-1824,
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.