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 - The National Library of Ireland has microfilms of virtually all the church parishes B/M/D register.
For Pat(rick) Corkery M 1901 (exact) somewhere in Ireland, I found 1 rcd, Co. Limerick, Kilfinane CR.
For Marg(aret) Boohan M ditto, I found ditto. These are likely rcds for these ancestors. A view of the detailed M rcds should show they married each other. If so, then the view MAY show their parents' names as well as other info.
For Pat(rick) Corkery B 1876 +/- 4 yrs, Co. Limerick, with the father's forename unknown (or found on the M rcd) I found 3 rcds: 2-1872, and 1880. One of the 1872 rcds is in Kilfinane CR district. Father's forename for this rcd is Edmond. This is likely for your ancestor.
For Marg(aret) Boohan B 1880 ditto, I found 3 rcds: 1876 Kilmallock CR, 1876 Bulgaden RC, and 1879 Mahoonagh RC parishes. Father's forenames were Cornelius, Cornelius, and James respectively. One of these is likely for this ancestor.
For Edmond Corkery M 1868 +/- 4 yrs, Co. Limerick, I found 2 rcds: 1867 Bulgaden RC, and 1867 Kilmallock CR. These may be church & civil rcds for the same event. Info found on the B rcds above SHOULD let you pick which, if either, is for this ancestor.
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.