Cowboy Junkies have made several albums. I have some of them, so I don't think they could be considered a one hit wonder. But I'm not here to argue.
Are you from Canada?
I'm not sure if this was ever hit, but it was featured in the movie "Natural Born Killers". It was originally done by the Velvet Underground in the '60's. The Cowboy Junkies haven't had a lot of commercial success outside of Canada, but I love them!
Or so I've read.