You are lucky. Most of the forenames you listed are fairly rare in Ireland.
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 Terence McGowan B ???? in Co. Leitrim with a father forenamed Dan(iel), I found 2 rcds within your timeline: 1852, and 1855, both in Kinlough parish.
For Rose McGowan B ???? ditto, I found 2 rcds: 1851 and 1858, also in Kinlough parish.
For Barbara McGowan B ???? ditto, I found 1 rcd in 1849 ditto.
For (Kate) Cath(erine) McGowan B ???? ditto, I found 3 rcds in Kinlough: 1858, 1860 and 1861.
For Bri(dget) McGowan B 1849 +/- 4 yrs in Kinlough parish, Co. Leitrim with a father forenamed Daniel, I found 0 rcds. The only rcd meeting these criteria is in 1857. This seems to fit your timeline.
A view of the detailed B rcds SHOULD reveal the parent's names, to include Rose's maiden name. With this info, you can search for the parents' marriage rcds, likely in the same parish. Marriage rcds USUALLY show the parents' names and other usful info. This will take you back another generation if you are lucky.
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.