Petrol stations can be found every 3-4 kilometers on the main road around the island of Rhodes and in almost all the villages.
Thy accept cash, but credit and debit cards can be used too.
The working hours are from 08:00h to 20:00h and after that there are lots of automatic ones that you can use any time, so refueling your rental car will not be a problem in Rhodes.
Fuel stations are not self-service during the working hours so refueling your car is very comfortable, you only need to say to the employ that will approach your vehicle how much fuel you will need, and he will refuel your car, you only need to open the tank for him.