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 Thomas Hicks B 1866 +/- 2 yrs, Co. Cavan, with the parents' names unknown, I found 3 records. NOTE - NONE are in 1866 exact.
Civil B/M/D registration was mandatory after 1862. Suggest you query the General Register Office at WWW.GROIRELAND.IE for more info.