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 available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome), and the National Library of Ireland on microfilm.
For Ann() Feeney B 1857 +/- 1 yr, somewhere in Ireland, with the father's forename unknown, I found 5 rcds: 1856 Sligo, 1857 Roscommon, 1858 Galway, and 2-1858 Sligo. Father's respective forenames were James, Michael, Michael, John, and Andrew. You will need an exact DOB, parent(s) name(s), and/or placename(s) to pick which, if any, is the right one. Offhand, the 1857 rcd seems the most likely.
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.