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 Sarah Roach B 1865 +/- 4 yrs, somewhere in Ireland, with the father's forename unknown, I found 4 rcds: 1862 Kildare, 1864 Galway, 1866 Tipperary, and 1868 Mayo.
For Pat(rick) Bohan B 1864 +/- 4 yrs, Co. Roscommon, ditto, I found 1 rcd in 1867, Roosky CP. Father's forename was Michael. This MAY be for your ancestor. You will need an exact DOB, parent(s) name(s), and/or placename(s) to learn if this is the right record.
For Mic(hael) Bohan M 1860 +/- 4 yrs, Co. Roscommon, I found 1 rcd in 1862, Kilronan RC parish.
For Mic(hael) Bohan B 1837 +/- 4 yrs, Co. Roscommon, with the father's forename unknown, I found 1 in 1839, Kilronan RC parish. Father's forename was Thomas.
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.