Wheelchair Carrier?

First the bad news.
Your Prius is rated to 825 pounds of passengers and cargo, if you have 300 pounds of wheel chair on the back you are left with 525 of passengers and other cargo. You can overload your Prius very easily.
Toyota does not rate the Prius for towing.

Now the good news: there are receivers for the Gen 2 Prius in both 1 1/4 and 2 inch here is one
Torklift Central | Torklift Central | 2004-2009 Toyota Prius Gen II EcoHitch
That will let you mount your wheelchair carrier, be very aware of weight issues and that you tail/brake light still show!

Check to be sure which size you need before ordering.

 

Yes, technically the chair and the carrier would exceed the tongue weight of the hitch.

That leaves you with several options: Get a different vehicle with a higher tongue rating for the hitch. Or use a small trailer to transport your chair.

 

200 pounds is not a limitation of the hitch but to where it connects to the car. The Prius was not designed to tow.

 

You could take the weight off the Prius.
Access Mobility Scoota Trailer for Scooters and Power Wheelchairs | Access Mobility Equipment
Electric wheelchair trailers-” The Scoota Trailer ” Scooter and Power Wheelchair Trailer | Affordable Mobility
Swivelwheel-MOB electric wheelchair & scooter trailer
I have not used any of these

 

60 pound aluminum hitch mounts (I see 4 wheel powered wheel chairs under 120 pounds, which gets you under 200)

amazon.com/Cargo-Carrier-ramp-Wheelchairs-Dimensions/dp/B001ODSGD0
amazon.com/Five-Star-436-ACC-TG-Carrier/dp/B0034KBCAU/

 

158 + 60 is certainly close. (Since 60 pounds is the shipping weight, it will be somewhat lighter out of the box) I found a 54 pound shelf, but the reviews said the supports were too far apart for their chairs, so I did not show it earlier. Does your chair have very large tires?

amazon.com/Husky-81150-Aluminum-Mobility-Wheelchair/dp/B00GJLYN9I/

 

Jimbo makes a good point. It's a little bit over spec, but I don't think it would be a problem so long as you drive appropriately, understanding the handling of the car will be reduced with 220 lbs in the rear. The main thing to watch out for would be to take large bumps more slowly, to not stress the hitch. Or if you installed something like a roof rack with a couple of bungee cords, you could take 20lbs of force off of the hitch easily enough. Obviously, do this at your own risk.

If you wanted better handling you could fold the back seats forward, move the spare tire to where the front passenger's feet would be, and remove all of plastic parts and carpet for the hidden compartment in the trunk. All of these things will help shift the center of gravity of the car forward to maintain its handling. Then if you carry anything heavy in the car, place it in the front or rear seat instead of the trunk if possible. I would also probably run equal tire pressures on all tires in this circumstance (instead of airing the front tires a few Psi higher per the door placard) as the rear tires will be bearing additional weight.

 

I carry a push mower on a rack that goes in the hitch on my focus. You really don't want to much weight because the leverage of where it connects to the car frame is severe. I wouldn't do more than 150lbs.

The other thing you could do is have some other supports for the hitch mounted to the frame or bumper bar perhaps. 300 lbs is just a lot of weight to be hanging off the back. Think of the stress when on a bumpy road.