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 Elphin parish, B rcds begin in 1808 and M rcds in 1807. There is no certainty that ALL rcds created after these dates survived, or that ALL events were rcd'd.
For Tho(mas) Hicks M 1831 +/- 2 yrs, Co. Roscommon, I found 0 rcds.
For Bri(dget) Kelly M ditto, I found 14 rcds with 1 in 1831 in Elphin parish. It is unlikely (but not unheard of) for the the IFHF to transcribe one party to a marriage, but not the other. If you think there is a transcription error, contact firstname.lastname@example.org.
For Peter Hicks B 1833 +/- 1 yr somewhere in Ireland with a father forenamed Thomas, I found 0 rcds.
You state you have the baptism info on Thomas and Bridget's children. You should share this with the IFHF so it can be added to the database.
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.