That's a useful map! Thank you. Actually, after reading even more of the Manx Notebook, I am wondering if the name is a corruption of Ballalionney, farm of the glen, Kirk Michael, or Ballalheaney, Meadow Farm, in Andreas (or Ballalona, Ballaleney,Ballaleaney, Ballaihonna all around the island, all meaning glen farm or meadow farm. The writing on the document is pretty clear. I will search for the farm on your map.
Susan