Actually when I asked about that they told me that the person buying the car plus the spouse will be the guarantor. If you are buying new the dealer does all the paperwork and will get a response in I think they said 24 hours.
When I had asked about a long term rental it was the same as short term rental but my sister has since found a no name car rental company with really good prices and service, and if she considers the prices really good they must be excellent. I would try to buy first but if you like I can ask about the contact info for this car rental.
If you own a property you do not need a guarantor but if you are renting it is now very difficult to get finance on a car. Too many people have simply abandoned cars at the airport still owing large amounts of moeny on them.
My husband stood guarantor for a so called friend who then left the island having not paid anthing for several months.
The bank were going to send the car to auction where it would have sold for less than was owed on it and we would have have had to pay the remainder. My husband bought the car from the bank for the full amount owed and the garage we bought our car from sold it for us for a profit so we didnt lose in the end but we could have done. It was only because the owner of the garage was able to pull some strings with the bank on our behalf that we able to get out of the mess.
As for long term rentals you can get them if you know where to go but some rental companies will try to get you to pay the same as for short term.
As I said before, you just need to look around and play them off agaisnt each other. Most car rental firms have had a very season and are happy to get anything. Maybe in Nicosia it is different but in paphos there are so many rental companies with it being a tourist area that they are fighting for whatever they can get these days.