You might start with "Candlemas Eve" -- it starts with Brigid but goes right on through Whitsun. The tune and words are also in the Oxford Book of Carols, as I recall.

Also, elsewhere on the forum I posted the words to my friend Jon Berger's John Barleycorn/Easter Carol. If you like that one, you can download the song (and the rest of our one album, for that matter) for free from Jon's Web site. Side 1 (this side has Jon's "Spring carol" on it, which you might like, but it is May-ish rather than Easter-like, plus it's pretty Christian in tone) is on this page, and side 2, with the John Barleycorn on it, is on this one.

Of course, there's always "Jack in the Green."

And there's another (totally secular) one I love, by Dillon Bustin, that's posted on Mudcat: "Gardening"

Cheers,
Claire