Almost as soon as I sent the message above, I remembered that I had posted elsewhere last fall about this and gotten a reply that seems to work.
Another researcher said when he can't find a place name, he searches in the known area, in this case Craddanstown. Right next to Craddanstown in the Tithe Applotments is Ballynaskeagh. He guessed, and I suspect he is right, that Balnahee is a phonetic spelling of Ballynaskeagh. '-skeagh' is pronounced 'skee'.
Several of my family names, including the most important, BRUTON, are in this area as you noted, Annette. So this is my best bet.
I see Ballynaskeagh in the 1901 and 1911 censuses but can't tell what Catholic parish it would be in.