You can also try Budget,
www.budget.co.th
I think they also have free delivery to your hotel in Patong or whereever you want to pick it up.
We had a lot of cars on the beach road before tsunami, they were cheap to rent but had no insurance. I would stick to the bigger chains, like Budget or Avis.
Phuket Gazette often have ads with cars for rent on monthly basis, it may be your best option if you look for longer term.