Spinning a barrel is not too difficult, provided you *DO NOT* intend to try and use it on the field.
2" ID AL tube.
1" ID, 2" OD ball bearings.
Slot the 2" ID tube to allow for a belt to be looped around the barrel.
Mount the tube to a fixture of any sort.
Use an Automag valve to fire the ball. Chop the Mag body and rail so it lines up with the barrel suspended in the bearings.
Use a small motor to drive the belt/barrel.
I think that will do what you want. Though it will be a single shot contraption.