Alright, I just got this figured out myself.
Our car is a Toyota Yaris and the only hitch options I could find were for a Class I receiver. Class I (1-1/4") has a tongue weight of 200 lbs. Understandably, they don't really make full-size motorbike carriers for Class I since with even a small motorcycle you'd typically be way over the tongue weight. Also, if you're hauling mopeds, motorcycle carriers are overkill.
So with some digging I found a small company that hand-makes a Class I hitch carrier for small motorbikes . Don't be fooled by the Web 1.0 site - they are real. I ordered and they shipped out the next day.