Sparling's "Irish Minstrelsy" (1888) has "Song of an Exile" by James Orr and gives the following note on the author:

Weaver, rebel and poet. Born in Ballycarry 1770; died April 26, 1816. Contributed to the Northern Star, became a United Irishman, fought at Antrim, went into exile and on the outward journey wrote "Song of an Exile". He soon returned to his home, however, and his loom, where he remained until he died. There is a monument to his memory in Templecolman churchyard, near Ballycarry."

Sounds like your man! I'll try scanning in the words if I get a chance over the next few days.

I have no idea where Ballycarry is - John Moulden may well be able to help.

Regards