Thanks to Andrew for sending in his DIY Remote Control Ping Pong Ball Machine Gun. The mechanism he used reminds me of the type that is normally used to launch baseballs and tennis balls. Even Nerf Gun Darts are fired using a similar method, I guess if the method works there is no need to make a better mouse trap. This system is controlled using an Arduino microcontroller and is fired by sending remote commands to it. 

“The electronics for this project are simple.  They consist of an Arduino, a stepper motor, a ULN2003 driver chip and a couple of LEDs.  I based the circuit off of my previous project “Easy CNC Controller“.  I chose to use this method as it was very easy, and requires no additional parts.  I got the motor from an old scanner.”