Scooters are a great way to travel around Yakushima especially if you are alone. They can be rented at these places. All models are 50cc scooters:
In our experience Suzuki Rentalease in Miyanoura is the best. They are a local company who have been around for a long time. They offer 24 hours rental for 4000 yen and are used to renting to non-Japanese. You can book directly with them in English by email and make your language simple and clear.
You Shop in Anbo offers 24 hours rental for 3500 yen. The selection is good but no English is spoken and I wonder how interested the owner is in foreign customers, as after so many years he still offers nothing in English.
Yuko Rental is new and offers 24 hours for 3500 yen. Try emailing directly - although we never had any replies to our emails!
For more information about Yakushima accommodation check out the one and only Yakumonkey Guide to Yakushima