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 Felix Denning M 1903 (exact), Killinkere, Co. Cavan, I found 1 rcd.
For Marg(aret) Mary Doughty M ditto, I found 1 rcd.
For Marg(aret) Mary Doughty B 1885 (exact), Killinkere, Co. Cavan, with a father forenamed "Joe," I found 1 rcd.
For Felix Denning B ???? Co. Cavan, I found 0 rcds. There are NO B rcds for this name anywhere for any date in Ireland. The closest is a "Felim" Dinnem Baptized 1904, Killinkere RC, Co. Cavan, a son perhaps.
For Jos(eph) Doughty M 1870 (exact), Killinkere parish, Co. Cavan, I found 1 rcd.
For Maria Smith M ditto, I found ditto. A view of the M rcds SHOULD show their parents' names as well as other info. This will help you identify the correct B rcds.
For Jos(eph) Doughty B 1845 +/- 4 yrs, Co. Cavan, with the father's forename unknown, I found NO rcds. The closest feasible rcd is in 1829. Source notes don't state the start date for B rcds in Mullagh.
For Maria Smith B 1849 ditto, I found 4 rcds: 1846 Kingscourt RC, 1846 Cavan CI, 1851 Knockbridge CI, and 1853 Killinkere RC. Father's forenames were John, William, William, and Stephen respectively.
Working on just the RC rcds from above:
For John Smith M 1844 +/- 4 yrs, Killinkere RC, Co. Cavan, I found 2 rcds - both in 1844.
For Stephen Smith M 1847 ditto, I found no rcds earlier than 1852.
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.