As far as I know (and I have been attending the tennis matches here since the 90s) they don't really "organize" autograph signings for the Qatar Open.

If you purchase court-side seats then you can probably get an autograph and/or photo with the winning players after the match is over. Fans also crowd around the stadium exit (beside Gate 3, I believe) to greet players as they leave. Sometimes the players are also seen out and about on the Khalifa complex grounds. That's usually how I get to meet them.

Getting autographs here is a matter of patience -- and sometimes stamina! I'm getting too old for that though. ;>