"The Fiddler of Dooney" was set to music by Jo-Ellen Bosson. On a visit to Ireland, I mentioned this to an Irishman, and he seemed shocked at the thought of anyone tampering with Yeats's poems. Never had the opportunity to play the song to him. It's on "Return to the Land" by Gordon Bok, 1990.

Bok himself has set many poems to music, for example:
"The Sea Wife" and "Harp Song of the Dane Women" by R Kipling
"The Death Ship" by B Traven
"Sailor's Carol" by C Causley
"The Liza Jane" by J B Connolly (uncertain, he says he had found it in a book by said author)
"Sally" by J Goodenough
"Little River" by R Moore
"Peace on Earth" by W C Williams

From my own country, the poems of G Fröding, E A Karlfeldt, and Dan Andersson have been set to music by many different composers.