Church records are always a good place to start. Anyone with a Scottish ancestry would be a Presbyterian so I would try Second Newtownhamilton Presbyterian Church Microfiche available from PRONI with minister's consent.
Also on the PRONI site check out the Ulster Covenant (South Armagh constituency) for Kinnears. That might be your great grandmother's signature!
Your father is the same generation as mine. They only lived 5 miles apart.I will ask him if he remembers your father.