Just tried it myself using Firefox. Did not log in. On the "Select Car" page, no cars come up.
ETA: I edited my reservation info and changed the pickup/dropoff location to the Car Care Center and then tried the Dolphin and both work. Then I edited it again to set it back to MCO and again, no cars are shown on the "Select Car" page.
ETA: I set it back to MCO but changed my pickup date by one day and it works. Set it back to my original pick up date and again, no cars.
ETA: Played around a bit more. It seems to have a problem if the pickup day is a Sunday. If I change my pickup day to Sat or Mon, it works fine. I tried a few other Sundays in May and got the same result each time: if I try to rent a car at MCO on a Sunday in May, it shows no cars.