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 Pat(rick) Gilmartin B 1828 (exact), somewhere in Ireland, with the father's forename unknown, I found 4 rcds: all in Sligo. Father's forenames were John, James, Mich(ael) and Mich(ael). Another 20 Patricks were B within a +/- 4 yrs range. You will need an exact DOB, parent(s) name(s), and/or placename(s) to pick which, if any, are for your ancestors.
It would help if you knew Honora's maiden name as a marriage is far more conclusive if found.
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.