MacLysaght’s “The Surnames of Ireland” says the surname in Gaelic was Mac an tSaoir (meaning son of the craftsman) which was sometimes anglicised as MacAteer. He says: “An Ulster name for which the Scottish MacIntyre, of similar derivation, is widely substituted.”
So MacLysaght reckons the name is an Ulster name (obviously that includes Co Donegal); your ancestor reportedly gave Donegal as his place of birth, plus McIntyre is almost unknown in Cork. For me, this all tends to point to Donegal as being the more likely origin than Cork.
The underlying problem, and the probable reason why you cannot locate the family, is simply that there are no comprehensive records in Co Donegal for the 1830s and 1840s to search. The churches weren’t recording baptisms and marriages in most parishes in Donegal then. No easy way round that.