Joe Riley was a Texas Ranger working out of 'Laredo'. Previously he had been a gunfighter who sometimes found himself on the wrong side of the Law. In fact, he joined the Rangers just so he could escape the ire of a local sheriff.
But Joe Riley didn't remain a Ranger for too many years - eventually he struck out to make his fortune and found that Lady Luck particularly smiled on him while at the poker table. By the early 1900's, Riley had made enough money at poker to buy into the great marathon poker game held on Commordor Duvall's riverboat.
His luck didn't hold out long, but he at least was as good-natured about it as he was when he was a Ranger under Captain Parmalee's command. He enjoyed a front row seat at the final game of the marathon.
His propensity for getting into trouble with the Law followed his family down the line like a curse. Somewhere along the Toobworld timeline before we saw him again in the "Maverick" movie, Joe Riley got married and had at least one child, a daughter. She married an Italian immigrant, probably a member of the Black Hand. His name was Falconetti. Their grand-child grew up to be Anthony Falconetti, the scourge of the Jordache family (as depicted in 'Rich Man, Poor Man'.)
Happy Trails To You!