I search the IFHF's online database at ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Records before 1863 are increasingly sparse. By 1800, they are almost non-existant. Many B/M/D events either weren't recorded, or haven't survived.
For a Tho(mas) Farrelly and Mary Reilly marriage, 1875 (exact), Co. Cavan, with the parents' names unknown, I found just 1 record. This MAY be for your ancestor. A view (usually at a small fee) of the detailed record SHOULD show their parents' names and other details.
Will leave it to you to search for the children born in Ireland, Thomas and Mary's parents names, and birth dates.