I have a copy of the Four Irish Songs Mick mentioned earlier (it cost me a lot less than the price he quotes!). The words consist of the first two verses only, and are indeed by Edith Wheeler, sister of Charlotte Milligan Fox and Alice Milligan, but the air is not a Munster tune. According to the booklet "The melody to which the words were written were taken down from William Simpson, of Moneyrea, one of the few remaining handloom weavers in Co. Down. He played it upon the fiddle, and called it "The Banks of Claudy."
The three sisters travelled together collecting songs and tunes in Ulster around 1909, and published the book of four songs in 1910 with arrangements by Charlotte Milligan Fox. The songs are beautifully illustrated by Seaghan MacCathmhaiol [John Campbell, brother of the poet Joseph Campbell].
Cathal O'Byrne and Francis McPeake, who were mentioned above in association with the song, were part of an informal group which also included Roger Casement that used to meet at Francis Bigger's house in Ardglass in the years before the First World War and the Rising, and Colm O'Lochlainn got many of his songs there. I don't know if Edith Wheeler, who was a staunch Unionist, ever participated in the social gatherings at Ardglass, but I believe her song could well have been performed there.