We decided not to rent scooters. But I did get the info on the cost. I'm including it here because I could not find the rates online anywhere.
The major scooter rental company appears to be Gibson Scooters. Their phone number is 423-7445. They advertise rates of $55 for 8 hours and $75/day. The hourly rate is $25 for the first hour and then $10 per hour for extra hours. (A day car rental is less expensive!).
These are regular scooters, not mopeds like you can rent in many places. There are no mopeds available on the island. All of the scooters can carry two people.
There are also scooter rentals available all along the Cable Beach strip. I did not get their prices.
Gibson Scooters doesn't take American Express, or Visa, MasterCard or Discover either. They accept cash or traveler’s checks only, no credit cards.