Riley and its variants (Reilly, O'Reilly etc) is one of the most common names in Ireland, so unless you have some idea of the area where he came from, I'm afraid it will be literally the proverbial needle in a haystack.
Passenger lists of immigrants to the US might show his port of embarkation which would possibly narrow it down a little bit. I'm not familiar with those records and don't know if they ever show place of birth, but it would be worth a try.
