Just A suggestion of where you might try if he had a social Security # you could request a copy of his application.
Also His Obit might list Brothers and Sisters. Pull up all the Smiths in the area where he was born in 1880. And try to see if you see any paterns in name of Children I have found that in almost every family the oldest children are named after the Grandparents. If that doesn't work you would have to go to Probate records If you know his mothers name search for a marriage record on her.