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 county, 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 Rose McCloskey B 1840 +/- 4 yrs somewhere in Ireland with the father's forename unknown, I found 10 rcds: 1837 Tyrone, 2-1838 Louth, 1838 Armagh, 1838 Antrim, 1839 Louth, 2-1840 Cavan, 1841 Cavan, and 1844 Louth. For the 1840 Cavan rcds, the father's forenames were Mich(ael) and Pat(rick). You will need an exact DOB, parent(s) name(s), and/or placename(s) to pick which, if either, is for your 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.