So far as I can tell, it's a Canadian variant (possibly via Ireland) of John Barleycorn: a set of lyrics is at  The Donnellys by James Reaney.  I don't know how close it might be to what you're looking for, but it's a start.  There's a recording available on Sandy Paton's  Folk Legacy  label:

The Barley Grain for Me  -Margaret Christl and lan Robb with Grit Laskin.  There's a short sound sample there, too.