I just did a google search myself for you and found this one.
http://www.discountmobilityusa.com/land_scooter_rentals.htm
It's $175 for a week. They also have canopy's that you can add for an additional $15 per week per scooter. Might help with that Florida sun to help shade them a bit. My mother in law didn't care for the canopy since she's a bigger lady and it would cut into her where it attaches to the scooter, but I would think if your parents are of "normal" size, then they would have no problem with it. You can also remove it yourself if it's bothersome.
This is the site that we rented from last year.
http://www.scootorlando.com/
Their prices range from $25-40 per day, depending on what type of scooter would fit your parents best. They all have different weights on them, so make sure to know roughly how much they weigh, cuz they ask you. All these (except the "dream" will fold down to fit in a trunk, etc. IF you are driving, and don't have one already, try to get a handicapped placecard. This will let them park very close to park gates and save YOU lots of walking! If you don't or can't get one, try for the AAA parking pass. You can buy them right off ebay for pretty cheap and you park right behind the handicapped parking.)
Good luck finding the right place to rent from!