That one can rent on an hourly basis. 

So there aren't any? 

Try Phuket Country Club Old Course in Kathu. They have courts that are rarely used and may be open to the public for a charge.

There is a tennis court in Samkong. Close to Bangkok Hospital. Moban behind the hospital

There are private courts in Chalong which rent by the hour. Probably have to do a search for their name.

As mentioned above, there are available courts at PCC. And many major hotels in Patong rent them out by the hour.