I should point out that I gave the chorus slightly wrong - it should go O Mary we crown thee, not "praise thee".

With a little bit of juggling you can use the tune for Molly Malone, and vice versa...

Apparently the song was written by a Mary E. Walsh, was called the Crowning Hymn, and was first printed in a collection (the Wreath of Mary), in 1883. (I got that from here, which has some interesting stuff about this whole topic, though I don't agree with too much of it.)