DC motor as rotational speed sensor?
Small stepper motors, like those found in old floppy disk drive for the head movement, are nice encoders. They produce two signals 90 degrees out of phase, which can be easily counted with an up/down counter.

Now both steppers or DC motors needs some torque to rotate, and coupling the trackball to a motor is not simple, and makes the trackball very uncomfortable.

I'd investigate another solution: Take one of those optical mice, tear it apart, and make it 'look' at the trackball. No friction! Those optical mice are very cheap, and are very precise. And no problems with slow speeds. Ideal would be just under the ball, so the movements would be just the inverse of the operators'.

Those optical mice are really a great invention...