Of course there's no evidence that Mrs. Knipp wrote "Barbara Allen," but somebody must have, and as an actress she at least had an interest in words and (as Pepys tells us) she could sing as well.

You're correct that had the song been part of a stage play, there should have been some record of it, but I'm thinking in terms of a minor entr'acte of some sort.

But I'm not trying to make a case for Mrs. Knipp's authorship. I'm only observing that we really know nothing about the song's origin and that we can deduce nothing about it from Pepys's diary.

And here's a curiosity: Why (as Goose Gander notes) should a ballad called "Barbara Allen's Cruelty" be set "To the tune of Barbara Allen" if the latter is the same song? Is the "Cruelty" merely an elaboration? Was "Barbara Allen" originally the name of a wordless melody? Or are we dealing with another "Rose of Tralee" - two different songs with the same title?