There are companies that will rent power wheelchairs; they are listed in post #2 of the disABILITIES FAQs thread. You can find that thread near the top of this board or follow the link in my signature to get there.
Most of the companies will only rent power wheelchairs (with a joystick to drive) to people who already use one in their everyday life, but have chosen not to travel with it. We tried to rent one several years ago for DD because we didn't want to bring hers. The first questions were whether she owned a power wheelchair at home and then they needed all the different settings from hers to get it set correctly for her. Some of the settings include too speed when done different things like going forward backward and turning, how fast it accelerates when doing those things, how quickly it decelerates. In all, there were about 8 settings they needed from her own wheelchair. We ultimately could not rent one because the sizes they had were too big for her. She is a small young adult and has a very narrow chair.
If a power wheelchair won't work out, there are companies listed in the FAQs thread that rent
ECVs, which are driven with a sort of tiller arrangement. They are easier to drive than a power wheelchair and require little to no individual set up. If your child is an adult, you can rent an
ECV from an of the companies listed in the FAQs. If he is under 18, you can try Randy's- they will sometimes rent for older teens, but most of the other companies will not rent for someone under 18.
The companies only have adult sizes of ECVs, so sometimes very small adults find they are to big of a stretch to use.