I have found a couple of references to a slow air called "Bessy [or Bessie] the Beauty of Rossinore Hill" on two albums called They Love Music Mightily and Sounds from the North -- but those recordings presumably don't have words, so I guess they can't help you with the spelling.

According to the UK Ordnance Survey, there are several places in the UK named Overton, but I'm guessing your song is Irish, and I haven't been able to find an Overton in Ireland, nor can I find a good site that lets you look up Irish place-names.

I had better luck with the River Nanny, which seems to be in Meath. I haven't found a map of it, or a complete description of it, but Google finds over 100 references to it on the Internet.

And except in the title of the tune, I can't find any reference to Rossinore Hill, either.