If he was Irish he may have been Catholic. If so try and see if they don't have a Baptismal or Marriage record for him. You may be surprised to find out how well the Catholic church keeps up with these old records. If they do have Baptismal or Marriage records it is a good chance you'll find something.
How to find these Catholic records I don't know what to say except ask a priest. I got my entire Fontenot family tree from a book on the Fontenot family compiled from Catholic records by a Catholic priest.