Steve & Jonathan, thanks for the discussion on these "songsters". Here are links to two of the "Forget-me-not" songsters. The first one does contain some of these ballads. I could not find dates for either one of them:
This one was published in Boston, and contains:
"Barbara Allan", "Captain Ward" (?), "Lord Bakeman", "Lord Thomas and Fair Eleanor", "Mermaid" (p. 79), "The Turkish Lady". The "Barbara Allan" is a strange version to me. The following Songster does not seem to contain any of the ballads. There is a song in it entitled "The Fashions of 1847" which might be a clue to dating it.