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 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).
For Marg(aret) Bohan B 1850 +/- 4 yrs somewhere in Ireland with the father forenamed Cornelius, I found 1 rcd in 1847, Co. Limerick. A view of the detailed B rcds MAY show whether the mother's name was Ellen - this isn't conclusive.
For Cornelius Bohan M 1843 +/- 4 yrs somewhere in Ireland, I found 2 rcds: 1842 LIM, and 1846 LEI.
For Ellen Sheehan M ditto, I found 50 rcds, one of which matched those for Cornelius: 1842 LIM. However, there wasn't a match at the parish level of detail.
For Patrick Donovan B 1850 +/- 4 yrs somewhere in Ireland with a father forenamed Patrick, I found 3 rcds: 1846 LIM, and 2-1853 LIM. A view of the detailed B rcds MAY show that the mother's name was Catherine - note, this isn't conclusive; Catherine was a very common name.
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.