According to Bronson this ballad "has not been found among the English-speaking peoples" since before Sharp's time and, since the melody to which Anna Brown sang it in Aberdeenshire was not notated, he assumed that no traditional tune would ever come to light. However, the information from the site linked by Tim, that James Carpenter notated a version from Bell Duncan, at least gives us hope of a tune. It doesn't look as though the ballad had a significant history in Amercia, though.