We bought a used car from the main Peugot dealer. On the same road as Expert in Corfu. (Further down the hill toward the turn off to the port). The car was a couple of years old and they had a choice of a few. Last time we were there they had quite a few outside again.
On the same road going toward Gouvia there are quite a few dealerships as well as several independant second hand dealers with quite a wide choice.
Nikos at Peugot was really helpful sorting out all the things that needed to be done.
You will need a residents permit to buy a car. If somebody is willing to sell you one without then I'd be concerned about dealing with them. You don't need the green card version which is for working just the blue card permit which is relatively easy to get. One day I'm sure this will change.