Contribution by Liam Clancy, quoted by catspaw on thread 44455:

"'The Patriot Game' was written by Dominic Behan, but it was originally a song from the Appalachian Mountains ('The Merry Month Of May'). Then it became a popular song, slightly adapted by a popular singer of the day named Jo Stafford who called it the - What was it called? 'The Bold Grenadier,' or something.
And it was from that popular recording that Dominic Behan took the tune and he made it into 'The Patriot Game.' And of course we used to sing this with great passion at the folk clubs in the (Greenwich) Village. And among the patrons was a young singer/songwriter who came into town named Bob Dylan. And he transformed it, of course, into 'With God on Our Side.'" Actually Dominic Behan chided Dylan publicly for lifting Behan's melody until he was reminded that he himself had "borrowed" the tune. As for the phrase "God on our side," it might have come from Robert Southey ("The laws are with us and God's on our side") or from George Bernard Shaw's play Saint Joan."

Hope this helps ...