Note that the same trick works on plastic as well. You need to select a hole saw with fine teeth to work on plastic.
Once you have a piece of circular material, you need to cut a groove so the tire does not slip out. If you have access to a lathe, great! Otherwise, you will need to construct a tool to do this.
Measure the diameter of the hole of the wheel. This should be the same as that of the drill bit on the hole saw. Go to a hardware store and find a bolt, washers and a matching nut. With washers on both sides of the wheel, insert the bolt and use the nut to tighten everything up.
Now insert the other end of the bolt into the drill press and tighten up the chuck. Now you have a simple lathe. Turn on the drill press and use a tool to cut the groove. A sharp chisel that is narrower than the groove works.
Of course, if you want to save yourself all this trouble (and fun!), you can use plastic or aluminum wheels for model airplanes.