Petrol stations inside Kos Town are limited. If you are staying in town, keep an eye on the gauge and stop at a station whenever you pass one rather than waiting until you are running low.
Once you are on the main road that runs across the island connecting the towns, fuel is easy to find. Stations appear every few kilometres and cover the route well, so you will have no trouble topping up as you explore.
One thing that surprises many visitors: petrol stations in Kos are full service. An attendant will come out and fill the car for you. You do not pump the fuel yourself as you might be used to back home. Just pull up, tell them how much you want or ask for a full tank, and they will take care of it.