Aside from "Bonny Sweet Robin" being a song of its own ("Robin is to the greenwood gone"), the tune is also used for the carol "Come mad boys, be glad boys" (aka "Carol for St. Stephen's Day," providing a definite seasonal tie-in), and also for "Sweet angel of England." The tune can be found in the Fitzwilliam Virginal Book, also in Chappell, English Popular Music, Vol. 1, pp.153-4. Several nice clips on YouTube under the titles of "Sweet angel of England" and "Robin is to the greenwood gone."

There are many carol books scanned at Google Books which go back quite far, and I'd particularly recommend checking out some in French, where you'll find interesting tunes for carols almost never performed now, due to language difficulties. Prior to the 1800s (if I recall my QI trivia correctly), only 20% of the population of France could speak and understand the language/dialect we now know as French. But since you only need good tunes...