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 available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome), and the National Library of Ireland on microfilm.
For ???? Carroll offspring B 1852 +/- 10 yrs, Co. Ardfert, I found 0 rcds. Ellen and Jeremiah likely moved to either another parish, or immigrated to America.
For Ellen Griffin M 1842 +/- 1 yr, Ardfert RC parish, I found 1 rcd: 1842.
For Jeremiah Carroll M ditto, I found 1 matching rcd. These are likely for these ancestors. A view of the detailed rcds SHOULD show they married each other. If so, the view MAY show their parents' names as well as other lesser info.
For Jeremiah Carroll B 1817 +/- 5 yrs, Co. Cork, I found 2 rcds: 1820, and 1822, but not in Ardfert.
For Ellen Griffin B 1821 +/- 4 yrs, I found 8 rcds: 2-1817, 1819, 2-1820, 1822, 1824, and 1825.
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.