G'day Frank,Thanks again - it will be nice to have all the lyrics. I imagine that the song my friend was seeking was the Song of an Exile that Martin Ryan posted - written by James Orr as he left Ireland. That fits in well with the time (sung in Sydney in 1800 - Orr fled after involvement in the '98).
I suspect that your song The Exile of Erin is a follow-up by Orr, once he reached America, so it could also qualify, but narrowly. The style is very similar, and the texts really flow on from each other, So there would be a fair chance they have the same author.
BTW: You wouldn't, by any chance, have relatives out here in Sydney? There is a longstanding (now life) member of the Bush Music Club of the same name who has been known to apply his vocal chords to a few fine Australian songs over the decades past.
Regards,
Bob Bolton