If there is any sport that needs some sort of challenge system it is the fast action of basketball, especially college basketball. In virtually every game foul calls are made, or not made, that it is clear to every spectator is a wrong or missed call. I would like to see three types of challenges.
A coach should be allowed to challenge whether or not a foul is a shooting foul or where it occurred before the act of shooting. Whether or not a shooting foul indeed called was actually committed or whether a shooting foul should have should have been called. And finally whether or not a deliberate foul occurred.
Coaches should be allowed three challenges per half and one additional challenge per overtime period, but only when the team has a timeout left to risk. In other words if a coach losses his challenge he forfeits a timeout. Therefore coaches must be very careful about making a challenge appeal.
Thus it is very unlikely that a flurry of challenge will occur to slow down the game. Moreover coaches will be reluctant to call timeouts, wanting to preserve their right to challenge, and so such a challenge system might in fact speed up the game.