I said earlier that I didn't know where you could look. Have you tried familysearch.org? They have a lot of US records. And ancestry.com of course. Otherwise, you might have to narrow it down to the county they were in and hope the records were kept and are still around.
Was he a miner in the US? That might narrow it down to southeast Ohio, but don't hold me to it. I'm only going by memory, not by actual knowledge or research. Google '19th century mining in Ohio' or something like that, and see what it says. Add 'coal' if you want. I can't think of anything else they would be mining in Ohio. There weren't any mines in Cuyahoga Co. where I grew up, and I doubt if any in northern Ohio. And western OH is too flat.
Definitely try to figure out why his obit said 'Ohio papers please copy'. Throw the surnames or variants into familysearch or ancestry.com with location = Ohio and see what comes up for the 1860s and forward.
edit to add: include the surname Kirkwood, since they used that as a second given name.
