Copies of 'The Alewives Invitation' are available on the English Ballads website at Santa Barbara, University of California. I think they are all copies of the same sheet printed by Brooksby. Roxburghe dates it at c1672 but I think it's probably a little later. It is part of a whole set of ballads that utilise similar phrases around that time. However, the modern song is unmistakably directly descended from The Good fellow's Resolution also in Roxburghe c1680 and also on the same site. The earliest related piece I can find is by John Wade 'A Caveat for Young Men' c1666-78 again in Roxburghe. There are all sorts of offshoots from these ballads printed in the next 2 centuries, one of them being 'The Green Bed'.