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. Without a KNOWN county, there is AT LEAST a 35% chance your ancestor's rcds aren't in this database.
For Owen Muldoon B 1836 +/- 4 yrs, I found 0 B rcds in the existing database. The closest are 1829 Meath and 1830 Tyrone. You may want to refine your est DOB and do another search.
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.