My band used to play this song. Here's what I know about it:

The Creggan White Hare is an Irish hunting song in which the hare foils all attempts at capture. We got the song from a recording by Andy Irvine who considers it song a fairly modern, local ballad. According to Andy Irvine's book, Aiming for the Heart, he fleshed out the words and wrote a new melody for it. Andy says he learned it from an old BBC disc recorded in 1952 by Sean O'Boyle and Peter Kennedy. The singer was Vincent Donnelly from Castle Caulfield, County Tyrone.

Regards,
Radriano