I found a pack of neodymium magnets at Wal-Mart that looked like they'd fit inside the spokes of the rotor, and I bought some 26
Next, I used a power drill and a screwdriver handle to wind a pair of test coils. The coils were connected in series, taped to the top and bottom of the generator, and the rotor was spun up. Sure enough, a sine wave appeared on the scope.
After experimenting with different numbers of winds, I determined that a coil with 320 winds would yield between 3 and 5 volts, depending on how fast the rotor was spun. I wanted a pair of coils that could easily drive a simple linear 5v regulator for USB charging, so I figured two of these in series should work. I made a simple rectifier/5v regulator circuit and scalped a female USB connector from something less interesting.
The coils themselves only output 1.9 Watts at maximum rotor speed (0.25A at 7.5V), but I think this could be greatly improved by someone who actually knew what they were doing. A more efficient switching regulator and stronger, better-placed magnets would be great improvements.