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 parish, 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 Martin Duffey M 1890 +/- 4 yrs in Co. Mayo, I found 12 rcds: 2-1888, 4-1890, 2-1891, 4-1892,
For Mary Byrnes M ditto, I found 8 rcds: 2-1886, 4-1891, 1892 and 1894.
The 1891 and 1892 dates are common to both. Searching at the parish level for 1891 and 1892, I found a match in 1891, Annagh parish. These are likely for your ancestors. A view of the detailed rcd SHOULD show the marriage was to each other. The view should ALSO list their parents' names and other info. With luck, you might jump back two more generations using this database.
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.