Mr. Thomas Ramsey

1799 is long before the start of birth registration in Ireland (1864). To trace Thomas's birth you would need church baptism records. You haven't said what denomination he was but the only denomination in Tullyniskan with any records for 1799 is the Church of Ireland. If he was that denomination then the records start in 1794. There's a copy in PRONI (the public record office) in Belfast. I don't think they are on-line anywhere, so a personal visit may be necessary to view them. Baptism records for that period rarely have an actual date of birth, usually it's just the date of baptism which for members of the Church of Ireland might be 3 months or so after the birth.

Thank you Elwyn for the prompt reply. My guess is that Thomas was of Presbyterian faith but that would be a guess. I am not going to Belfast anytime soon living in virus infested Florida..
When he came to the states, he worked in the lime trade. Wonder if he may have learned it in nearby Coalisland?

Looking at the 1901 census for Derry, there were 43 homes and a population of 265. The majority were engaged in farming and linen manufacture. There were some coal miners (there used to be a small coal mine nearby) and general labourers. I don’t see anything specific relating to lime production but general labouring might cover that.

http://www.census.nationalarchives.ie/pages/1901/Tyrone/Tullyniskane/De…