RC marriages were only recorded in the statutory records from 1864 onwards. Prior to that you need to reply on church records, not all of which are on-line. Without some idea of which parish it can be tricky, but you could try rootsireland they have some Tyrone RC parishes on-line. PRONI in Belfast and the National Library in Dublin have copies of most surviving RC parish records, on microfilm, but there's quite a few in Tyrone and it would take some time to work through them all.
