All the big operators are here, such as Avis, Hertz etc, and their rates are probably "International" as well. Many smaller operators, such as "Highway Car Rent". I would be a bit wary about some of them as the insurance arrangements may not be what you expect.
The following Company has a good reputation, but I have never dealt with him personally. Send him an email, he will probably do a deal with you.
PJG wrote:Always use ThaiRentacar. They are reliable and use good new cars. They have a depot by the airport and their own web site.
I also recommend Thairentacar, I have used them several times with no problems. I don't recommend using budget, they were very fussy about damage (which wasn't even from me) and contract details.
I allways used ThaiRentaCar as well, but when I wanted to book for October, I noticed that they had raised their rates considerably.
Last year they charged me THB 1000,- per day for a Vios.
Now they ask THB 1500,- per day.
So this year I will try Quality Rent a Car. http://www.qualityrentacar.com