I don't recommend it. The roads on Cozumel are not the best and there is a ton of traffic at times - taxis, trucks, and the worst part....all the tourists who have rented cars and jeeps along with all the people on scooters. Lots of opportunity for accidents to happen since you have all these tourists who are not familiar with the traffic patterns or roads.
I rode a motorcycle everywhere for almost 30 years until I gave it up a couple years back, and with all that two wheel experience I would not rent a scooter on Cozumel or any other island.
But that is just my opinion.