Well, you can fill in the hole and re-drill it (you have a drill press and centering tools, right?), or you can enlarge the shaft (or a combo of both).
Its difficult to recommend a real solution because I don't know what kind of machining skills you have. For the sake of this discussion, I'm going to assume none, and that you have only the minimum of tools available.
In that case, the easiest would be to purchase a piece of wood dowel from a hardware store (Lowes, Home Depot, etc), which has a diameter equal to, or slightly larger than the hole on the wheel. Hopefully, this piece of wood will also be somewhat much larger than the shaft of the gearmotor output.
If the dowel fits the wheel, that is best. Basically what you do then is drill out a hole in one end of the shaft deep enough to receive the length of the gearmotor's output shaft. Then epoxy the dowel to the gearmotor, and epoxy the other end to the wheel. If the dowel is a little long, you'll probably want to pass it thru a "pillow block" style bearing (which could be as simple as a small block of wood with a hole drilled in it thru which the dowel can pass); doing this is best, because it keeps side-loads off the shaft of the gearmotor, which may not be able to take such loads long before wearing out. Remember to lube the pillow block with something like graphite (dry) lube.
If the shaft is larger than the hole in the wheel, then you have some work to do. If you have access to a small lathe, its easy - you essentially chuck the dowel into the lathe, and turn the dowel down a bit with a file, until it fits the hole in the wheel - then follow the steps above. If you don't have a lathe, then you could try to chuck the dowel into a regular electric drill, then clamp the drill to a work surface, and wedge the power button on, then use a file or rasp to turn it down some. Best way to know what size is needed it to use a caliper to measure the original shaft (you did keep it, right?), so you know what diameter you're aiming for. Be sure, whether you use the homebrew lathe method or a real lathe, that you wear goggles and gloves - NO EXCEPTIONS (and stand to the side as you work, because you never know what will break and be ejected from the spinning dervish).
Note that if you have a lathe and know how to use it - you can quite accurately do the end-shaft drilling of the dowel; otherwise you just have to be real careful to center the drill and keep it vertical in both planes as you drill the end of the shaft.
Now - if the end of your gearmotor's shaft isn't much smaller than the dowel, what you should do is use a larger diameter doweling, and turn down the end for the wheel, but leave it larger for the gearmotor shaft. Note also that this same technique (ie, building a coupling shaft) can be used for plastic or metal, although in the case of metal shafting, you would need to use a metal lathe to do the work, of course.
Another possibility - if you saved the original shafting - is to measure it, then go to the hardware store (or online) and purchase a piece of shafting (metal or plastic) that same size, but then use what are called "shaft couplers" to mate the gearmotor shaft to the wheel shaft. Here are some sites to look into for this:
Note that going this route may or may not be cheap, of course...