sand it down from 400 to 600 to 800(wet) grit sandpaper, prime it with quality spray primer, sand it again with 1200(wet) grit, paint it with the desired spray color, and apply a clear coat.
Tips and tricks:
While painting keep always like a span away from the surface. Apply light fast-moving coats, to prevent dripping, as it happens when the paint stays flowing in the same point for too long. Before painting the car, try before in a cardboard to "feel" the strokes and not dripping the paint.
To avoid any damage on the plastic, use water based spray paint if you can. Usually all brands are high pressure paint, for a begginer, you can try the Montana brand if you can, is very easy to use, specially the '94' kind, the matt colours, and they also have water-based too...
I don't know if there is water based spray clear coat, if not, I always reccomend using acrylic, because the solvents of the "normal" clear coat sprys sometimes react with the paint and mess the whole work, specially when working with plastics, which can do serious damage to the plastic sometimes.
If you keep the old ones, write down the voltage, amperage and size and sure you can find repairs, or make a holder for the new ones.
Consider grabbing one of those hoverboards, and you'll have more poweful motors and new lithium batteries, it will be lighter too, i think... That's an option!
Hope this helped! We want to see the pics of your son's "Rolls"