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 T(homas) Stafford B 1816 +/- 5 yrs, somewhere in Ireland, with the parents' names unknown, I found 10 records: 1812, 1813, 1814, 1815, 1816, 4-1817 and 1821. None are in Co. Cavan.
There are only 2,314 B and 1,137 M records ANYWHERE in Ireland at any date. These small numbers and the sound of the surname suggests it is of English origin; possibly from "plantations" in earlier centuries.
I have Staffords in my family lineage; they immigrated from England in the 17th or 18th century.