The Library of Congress, in its "Voices from the Dust Bowl" collection, has the text of a song called JOHN DILLINGER that was collected from Frank Lankas of Gardenville, NY, c1941. It looks like they don't have a tune for this, though:

JOHN DILLINGER

John Dillinger, Johnny Dillinger, the G-men will chop you down.
Some of the things that you've done done have been makin' the government frown.
Your number's up. The word's gone round you won't be goin' back to jail.
You'll be a bullseye for the police and they'll throw the lead like hail.

John Dillinger, Johnny Dillinger, the finger will be laid on you,
And the G-man watchin' with his gun is goin' to get you, too.
When he stops you, Johnny, he's gonna stop you dead,
And head you out for the Golden Gate packin' a load of lead.

Oh, Billy the Kid and the Dalton boys and others of their kin
Were bad gunmen outside the law, but they were brave gunmen within.
Now, you know the old-time story how Billy met his end.
It's too late to change you now. So long, old friend.