I research the Irish Family History Foundation's database. It contains 12,700,000 surviving rcds for abt 70% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
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 Martin Dowd B 1853 +/- 4 yrs somewhere in Ireland with the father's forename unknown, I found 6 rcds: 1850 Galway, 1853 Roscommon, 1855 Roscommon, 1855 Armagh, 1856 Roscommon and 1857 Roscommon. The 1853 rcd seems an exact fit to your criteria. The father's forename for this rcd is Martin. The parish was Croghan RC. A view of the detailed rcd SHOULD list both parent's names. This info is useful in validating the rcds below.
For Martin Dowd M 1849 +/- 4 yrs, Co. Roscommon, I found 0 rcds. Trying a broader search range, I found 1 rcd in 1840, Aughrim RC parish. A view of the detailed rcd SHOULD list the bride and parents' names. Ditto.
For Martin Dowd B 1824 ditto with the father's forename unknown, I found 3 rcds: 1822, 1828, and 1828. Father's forenames were Martin, John, and John respectively.
There are very few earlier rcds - you MIGHT find an M rcd for the 1822 Martin.
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.