Black jack, in Francis Grose' 18th c. dictionary of cant, etc., was a name thieves gave to the recorder, or receiver, of stolen goods.

More likely, however, is that the reference is to a gypsy's usual hair color.
A version in Sam Henry's Songs of the People calls them 'brown-eyed gipsys.'

Looking at Branson, "The Singing Tradition...," the original versions of this Child Ballad with 'Black Jack' Davy all seem to be American. I haven't checked this out thoroughly.