I searched 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. Thus, there is at least a 35% chance the rcds aren't in the existing database.
For Morris/Maurice Dunn and Elizabeth Coyle, I couldn't find matching M rcds for 1854, or a relevant range around this date.
For Mary Dunn B 1856 (exact) with a father named Morris or Maurice, I found 0 B rcds.
For Catherine Dunn B 1858 (exact) ditto, I found 0 B rcds.
I suspect info for your ancestors is in the mass of undigitized parish registers. It may take several years B4 this task is complete.
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.
Hope this helps. Good luck.