Actually, rethinking the requirements, it may be difficult to build this thing with your resources in order to get the belt fast enough to really blow away the competition.

My next suggestion would then be a Lord Kelvin water drop generator:

http://www.youtube.com/watch?v=3b23umXzPVA

Here you need only 3 buckets, two cans with the top and bottom cut off, and insulated wire. This, too, should get you in the 10kV range. You can easily demonstrate that you do all the work by hand, by manually lifting the bucket full of water to the height where you let it drain. Then two siphons or holes in the bottom of the bucket will let the water drain. One caveat here is that you would want to keep the amount of water used to a minimum, because water is heavy. Still, if everyone is thinking of a generator of a construction like you mention, no one is going to be close to the order of magnitude of your voltage, meaning your generator can be 100x heavier. Good luck.

———————————————————————–
Well, that's stupid isn't it–having a design competition where everyone has to use the same design–it's like having a race where everyone is required jog . . .

So this is an AC generator I'm assuming. Here is a schematic for a permanent magnet generator:

http://www.scoraigwind.com/pmgbooklet/itpmg.pdf

Essentially there is only one equation you need to know and that is Faraday's law of induction that:

V = -dΦ/dt

Where Φ is the magnetic flux. I don't know what level of science this is for, but what it boils down to is that if you take a loop of wire and change the amount of magnetic field through it, you get a voltage. You can compound it by making a coil of n loops and you multiply that voltage by n, but keep in mind that as you increase the number of loops, the loops are also getting further from the magnet, so the field strength is dropping. So the main contributions are going to be STRENGTH of magnetic field, the SPEED at which you change the flux, and the NUMBER of loops in your coils. A basic design would be to drill an even number of holes along the outside of a cd and glue a bunch of neodynium disk magnets of alternating polarity inside the holes and spin that as fast as possible between sets of coils.

That would create a generator like this:

http://www.otherpower.com/hamster.html

Imagine a very small diameter axle through the cd (a pen say, or smaller) and a string wrapped around it. Pulling on the string as hard as you can without breaking it should get it spinning rapidly.

If you literally can't use anything but wire and magnets, that would eliminate the use of the cd. In this case I would recommend dropping a heavy bar magnet through a large coil of wires. Again, the higher you can drop the magnet from, the faster it goes through the wires, the larger your voltage will be. This case may even produce a higher voltage than the above generator, but it will only produce a very large voltage for a very short time. This is the same design as the shake and charge flashlights. Depending on the type of measuring equipment available it may not be accurately resolved by the judges–if you are using a multimeter, say.
References :
http://en.wikipedia.org/wiki/Van_de_Graaff_generator

http://www.youtube.com/watch?v=algECMeQFrE