Hi Frances, I'd be willing to look at the digital image showing 'Kinegerye'. My e-mail address is david (dot) radcliffe (at) manx (dot) net
The Kine looks a bit like 'Kione' (head) with 'Garey', but I'm not sure...
Jenkinson's Practical Guide to the Isle of Man (Local Names XXV) lists a 'Kione Garee' which he translates to something like head of the swamp/bog/marsh... He doesn't say where such a place might be though.