Mark and SingsIrishSongs,
Thanks for all the dictionary digging and lyrics looking you've done.
As far as which came first, I think it might be the other way around. As I mentioned above Yeats probably used the traditional Irish song, The Rambling Boys of Pleasure as the basis for his poem. One of the verses:
Down by yon flowery garden, where me and my true love do meet I took her in my arms and to her I gave kisses sweet She bade me take life easy, just as the leaves fall from yon tree But I being young and foolish, with my own true love could not agree.
When I first read the words to the Willow Garden song, I thought it might be a parody. But I don't know about that.