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 Pat(rick) Feeny B 1892 (exact), Co. Sligo, with a father forenamed James, I found 1 rcd, Easkey parish. This is highly likely to be for your ancestor as it fits your info perfectly.
Nora/Hon(ora) - no rcd Cat(herine) - 1891 Delia - no rcd Mary - 1895 Bri(dget) - 1877 (this seems too early for your line). James - 1893
For James Feeney M 1887 +/- 4 yrs in Co. Sligo, I found 3 rcds: 1883, 1884, and 1888. However, the 1888 rcd wasn't in the matching rcd for Bridget.
For Bri(dget) Connolly M ditto, I found 2 rcds: 1887 and 1888. The parishes were Cloonacool and Castleconnor respectively.
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.