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 - Microfilms of parish church rcds are kept by the National Library of Ireland (NLI).
For Edw(ard) McDevitt B 1860 +/- 2 yrs, somewhere in Ireland, with the father's forename unknown, I found 6 rcds: 1858 Antrim, 2-1859 Derry, 2-1861 Derry, and 1862 Antrim. Father's respective forenames were Alexander, John, James, George, James, and Alexander.
For Mary Brady B 1862 ditto, I found 161 rcds - waaay too many to easily summarize here. None were in Co. Donegal.
Suggest you research naturalization rcds, church/civil marriage rcds, censuses etc., to find exact DOB, parent(s) name(s), and/or placename(s) to help pick which, if any, are the right rcds.
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.