As has already been stated, yes, you can rent scooters and you can also rent motorcycles, if you like bigger bikes.
However, if the only reason for renting them is to visit 7-mile beach, you can take public transportation, which is very regular and cheap. At $2.50 per person each way to anywhere on the island, it's a great way to get around. Even if you want to go to a couple of different places, it's still an easy cheap way to get everywhere. Of course, it doesn't beat the fun of tooling around on a little scooter in the open air as long as you don't have any problems, as scooters can be a little tricky for those who haven't done it before. Might want to make sure you purchase the travel insurance.