I would agree that Crayton is pretty well unknown in Ireland. (Just 2 in the 1901 census). Creighton and Crichton are the much more common versions with around 800 in the 1901 census. 48 of them were named James and 11 of those lived in Co Antrim. So James Creighton/Crichton is a common name in Co. Antrim, and will have been just as common in 1842. So you need to take care to find the right family.
You should try and find James parents names from his marriage or death certificates. (I assume he married in the US. I certainly don’t see a marriage to a Harriette Curtis in Ireland).
Statutory birth registration didn’t start in Ireland till 1864 so you won’t find a birth certificate for him. You might find his baptism but to do that you would need to know his precise denomination and roughly where in the county he came from. Plus as I say, you’ll need parents names. Otherwise you have no way of being certain it’s the right family.
Looking at the 800 in the 1901 census there were 249 Presbyterians, 318 RC, 204 Church of Ireland, 18 Methodist, plus some “others.” And some of no religion. So spread across the most common denominations.
You might get a lead on his origins from passenger lists, naturalisation papers, military records if applicable, a will or an obituary.
If you are unable to get a lead on where he came from, DNA testing might be a way of trying to find another family that does know a bit more about his origins.
