Searching for bonny blue-eyed nancy through the "Digitrad and Forum Search" (it works much better than the old "Lyric Search", which is rarely worth using any more -though it found it, too), I also found this previous discussion:

How Can I Live at the Top of the Mountain  in which John Moulden gives the traditional text as sung by Elizabeth Cronin, together with an earlier version noted in Scotland around 1826.  He makes the point that, though most singers today sing it quite differently from the way Mrs. Cronin did, they all seem to have got it from her (though in many cases, at several removes; I suspect that Cathal McConnell features quite strongly as a factor in its current wide distribution).  The best source for a written tune would therefore be the recent book dealing with Mrs. Cronin's repertoire, though I don't know how faithful to her melody the subsequent commercial recordings may be, having, I think, only heard Cathal's.  I would not relish the prospect of attempting an accurate transcription of that, but I'll give it thought.

Malcolm