It is hard to match the cowboy Junkies laid back sound which I like very much too. I have looked for quite some time and never really found anything.
Who can match Margo Timmens?
not really similar but nice are:
His Name is Alive - Last Night is my favorite of theirs
Ida - Will You Find Me? very good and hope you like it
fwiw, from the selections above Cat Power may match the mood of CJ the best...
good luck