Don't give up!
According to the OED a "green gown" is a good old-fashioned euphemism for 'a throwing young Lasses on the Grass and Kissing them' or as Anthony Munday put it even more clearly in 1602 "At length he was so bold as to giue her a greene gowne when I feare me she lost the flower of her chastity".
There is a lovely song 'The Gown of Green' (Roud 1085) which was sung by Jack Norris of Cuckfield, Sussex and also by the great English gypsy singer Harry Brazil of Gloucestershire.
The song derives from a broadside which was first published as a 'Sequel' to an earlier 'Gown of Green' ballad which referred to events in the American Revolutionary War.
There is an earlier Mudcat thread on The Gown of Green which has some useful information, but nothing about the origins for Graham and Eileen Pratt's song.
Matthew