The drills used in the pitching machine you linked to probably incorporate something like 500 Watt motors. The drills probably incorporate something like an 8:1 reduction gearbox, and spin at about 600 RPM. The wheelbarrow wheels used have a periphery of about 1 Metre, so they will fire a ball at about 600 Metres per minute, or about 36 KPH.
You would probably need 2 or 3 times that speed, but not necessarily much more power, by taking advantage of the kinetic energy stored by relatively heavy wheels.
Inflatable tyres would allow the wheels to grip the ball over a larger arc to accelerate it without recourse to the complication of springs to allow the ball to pass between the wheels.
So I would be looking for a pair of 12" pneumatic tyred wheels spinning at 1200 to 1500 RPM.
Car starter motors are usually relatively high powered, but designed for short bursts of use only. A wiper motor would go the distance, but, IMO, may not deliver quite enough power.
An old electric wheelchair or shopping buggy may yield all the wheels, tyres, motors, batteries and the electronic control gear for the motors you may need for the project. There's usually a few cheap ones knocking around on fleabay.
Wheelchair controls usually allow individual control of each motor speed ... spin bowling?
Wheelchair motors usually incorporate a gearbox with too low a ratio, so you may need to junk the integral gearboxes in favour of a single stage reduction gear, probably 2:1 or 3:1, maybe using cycle chain and sprockets?
