I did make some enquiries last year for someone who was coming out on holiday from England and wanted to hire a mobility scooter.
There are a couple of places that hire out scooter on Baris Manco Boulevard in Calis going up from the Water Taxi and walking away from the beach go up to the lights and straight ahead. Then go around the first roundabout and keep to the left and then before the second roundabout is one place and after that is another two.
Then there is also a scooter hire place, across from the Lukka Cafe Bar, between Aroma beach & restaurant & Obens restaurant. They are located at the Koca Calis end of the promenade
Focus Travel Agents on the prom just near the public toilets and taxi rank, also have one outside, with a "For HIre" sign Last season they were 35 TL per day to hire out. The one they had looked very modern and up to date.
There is also a place in the one way street in Fethiye that specifically only hire out medical equipment and mobility scooters. I ask there and they are 30TL per day, although the one for that price looked quite basic.
Prices seemed similiar in most places around 30-35TL per day.These were last years prices, so they may have changed this year.