Kim, thanks very much. I have already found several things of potential interest !
1) The 1817 Census of the First Ballmoney Presbyterian Church has a number of names that correspond not to my Harrison line, but to my McCloy line: - my gggrandmother Ann McCloy b~ 1812 who also emigrated to Thompsonville CT around 1853 - her brother Moore McCloy b~ 1805 - Moore McCloy's wife Martha McClarty - Ann's brother-in-law George Lamont (via younger sister Eliza who was not born until 1818).
I know these are relatively common names but it is interesting that they all appear in that census.
2) The 1831 Derry census has a family of Harrison's in "N.E. Liberties of Coleraine" Barony (right next to Coleraine Barony) that look potentially interesting (names John and Charles appear).
Can you provide any more information on either of those or point me in the right direction ?