Probably never. I hate to be a pessimist, but the first season didn't do very well, and so that combined with the company who did the first season selling to Paramount makes it unlikely that we will see the other seasons. I would suggest trying to find copies fans taped off the television.
The Young Riders - 1989 Ghosts 2-2 was released on: USA: 29 September 1990
The Young Riders - 1989 Daisy 2-15 was released on: USA: 2 February 1991
The Young Riders - 1989 Jesse 3-2 is rated/received certificates of: USA:TV-PG
The Young Riders - 1989 Gunfighter 1-2 was released on: USA: 21 September 1989
The Young Riders - 1989 The Talisman 2-18 was released on: USA: 23 February 1991
The Young Riders - 1989 The Peacemakers 2-14 was released on: USA: 19 January 1991
The Young Riders - 1989 The Littlest Cowboy 2-6 was released on: USA: 3 November 1990
The Young Riders - 1989 Dead Ringer 2-3 was released on: USA: 6 October 1990
The Young Riders - 1989 Requiem for a Hero 2-8 was released on: USA: 17 November 1990
The Young Riders - 1989 Face of the Enemy 2-20 was released on: USA: 6 April 1991
The Young Riders - 1989 Color Blind 2-16 was released on: USA: 9 February 1991
The Young Riders - 1989 Blood Moon 2-4 was released on: USA: 13 October 1990