On the subject of Songsters, if you go to Google Books and enter just the word Songster, wou will see a large number of titles, of which a few are fully viewable. One at least dates back to 1784. I looked in that one, but is seems to be mainly "show" songs, with just the odd "Scotch ballad". There are also many from the early 1800's.
I don't have time to check them all out, though.

(You also get lots of hits about songbirds, of course)