Lighter - the tune referred to in the posts above from Joyce was not his Banks of the Bann tune (#556, which you linked), but the tune for With My Love On The Road (#323), which is the Slane tune.

I had a quick look in Roud for versions of The Banks of The Bann, which I'm taking as Roud 889 - The Brown Girl (there are 2 others with The Banks of the Bann title - 2495, 3473) for versions with music, of which there were 9 (full tune). They all seem to have been notated relatively recently - I think Barry's in JAFL 18, 1909 might be the earliest. I had a look at 5 of them - Barry, Huntington (SotP), Peacock(SotNO), Shields (SRaT) and Creighton (MFS). Of these only Eddie Butcher's version in SRaT used the Slane tune. (The tune in Creighton is lovely though!)

When I looked for Banks of the Bann and Joyce it returned a text of RN3473 from his Ballad Sheet Scrapbooks, but not the tune.

Mick