And each of these rhymes can probably traced back to the bawdy "Bang Bang Lulu" rhymes.

By "each of these rhymes", I meant
Mary had a baby, she called him Sonny Jim

Miss Susie {Miss Lucy and all the other female names used} Had A Baby/His Name Was Tiny Tim

Miss Lucy Had A Steamboat {Miss Susie etc}

When Susie {Pepples etc} Was One

**

I don't think that "When Taffy Was A Welshman" comes from the same source as the other rhymes I've listed.