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 - The National Library of Ireland (NLI) has microfilms of parish church rcds.
For Jos(eph) Duffey B 1832 +/- 4 yrs, somewhere in Ireland, with the father's forename unknown, I found 6 rcds: 1828 Dublin, 1830 Meath, 1831 Longford, 1833 Limerick, 1834 Dublin, and 1835 Louth. Father's forenames were Thomas, Philip, Stephen, John, Joseph, and Brien.
For Elizabeth Duffey B 1828 +/- 4 yrs, in the same counties as for Joseph, I found 10 rcds: 1824 Dublin, 1825 Dublin, 1825 Longford, 1826 Dublin, 1827 Louth, 1829 Dublin, 1830 Meath, 2-1830 Louth, and 1832 Louth. Father's respective forenames were James, James, James, John, Pat(rick), Pat(rick), ???, John, James, and Richard.
For James Monroe M ????, somewhere in Ireland, I found 2 rcds: 1855 Armagh, and 1860 Armagh.
For Elizbeth Duffey M ditto, I found NO matching rcds with those for James.
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.