The tune Mr. Happy has linked to is a gorgeous rendition, played by Martin Simpson on solo guitar, of the My-name-is-Delaney one.

If it's any help, the Willie Archer version has been recorded by Joe and Antoinette McKenna (she sings it). I see it's now on a "Best Of..." compilation but I have it on one of their original LP's, though it's buried in a box somewhere and I'm not sure which one it was. Farewell To Fine Weather perhaps? They're certainly two quite different airs. Wish I could be of more help - I can read dots but still haven't learned that ABC programme, and in any case can't really remember Antoinette's version except that I liked it.