If you can mark the tires with a piece of reflecting tape (I don't really know how that would affect balance/performance) then you can probably detect rpms easily enough using a photosensor/emitter pair (just picking one out of the blue, like Digikey p/n QRD1114-ND, you'd have to check the datasheet to see if it is really suitable for the frequency you're looking at.) Once you've played around with the distance/LED current/Tranistor load you really could just read the frequency with a DMM, for example, the Fluke 87, if you have or can borrow one. If not, counters are fairly easy to make too. The hardest part is going to be messing with the tape and the sensor positioning.
If you have an old mouse, you could probably use the IR photosensor out of it, if you're handy enough.
j.