Keeping an eye on half way stops, I have read somewhere that there are hundreds of Coole recorded in the Isle of Man. Personally I think the Street directory add up as the best source so far.
If he actually went looking in Ireland, he might have become enchanted with the legends of Finn McCool but most likely he would gone visiting someones recent grave,
Tombstones from Ulster is a sister website of the Ulster Historical Foundation, and reports no Coole memorial inscriptions , just Cooley in Co Antrim in Holywood co down.
I am a bit slow in picking up the emphasis of an ee sound that gets spelt ey. If I was feeling brickwalled, I would explore that spelling Cooley as just possible an offshoot of some of his recent ancestors, the spelling possibly imposed by those that kept registrars etc. Someone else who knows the ulster scots language and dialects might offer thoughts to you on this one. Good luck anyway, jim