Strange that question should come up today, I caught a bit of a showing of Crowded House "Unplugged" at the weekend and that song was performed - but goddammit I forgot the name and original performers. The band is certainly Antipodean though. Sorry, not so helpful.
There were two songs played.
When Shane actually dies "Throw your arms around me" By Hunters and Collectors was playing, and when his body is taken away it is "There is a garden" by Archie Roach that is played.