Seosaimhin Ni Bheaglaioch sent me a scan from an unidentified songbook which appears to be for use in schools. The title given in this instance is "Moladh Chill Mhuire" (in praise of Cill Mhuire) and the first lines are from a girl (is caili/n beag mise). But alas, again there are three verses and no chorus. The notes say the author is unknown but the song appears to be from 18th century Co Cork. And yes, there is a Kilmurray in Co Cork as well as in Co Clare.

some lines of the song, as given in this document, are a bit different than given previously in this thread; for instance, second verse begins "Is ann do bhi/onn tuirling mioncholu/r is faoilea/n" (the / should be above the proceeding vowel)

I havent listened to any recordings since I last wrote on this discussion thread.