Thanks for the responses, but the songs in the DT aren't quite right. Maybe I'm remembering the first one, the one that starts "Where are you going?/I'm going to Lynn." Maybe the reason I didn't memorize it years ago is that it's about a lady in Lynn, not in Scarborough.

It would be hard to modify the verse and start using it, because what would rhyme with Scarborough?

BTW, the format of that song, in which a third party tells a story about a devil and a damsel, is an older form than the others, where the lady herself does the talking. I have read that there has been tendency over the centuries for ballads to change from the narrative, third peson to the lyrical, first person.