Miami Beach, FL U.S.A

Concrete tennis court is basically a concrete slab-on-grade with some special requirements.
The main limitation is the need for very flat and uniform surface.  Usually, concrete slabs require joints (cuts in the concrete) every 8-10 feet in order to prevent uncontrolled cracking.  they also allow some variation in surface flatness (which is fine for walking or applying carpets...)  Tennis courts cannot have that, so a higher quality concrete with reinforcing steel are required.
I would find a contractor who already did many tennis courts and can show a track record.  Go see his past work and ask the owners about him and the finished court.

Proper preparation of the "base" is also critical.  It must be compacted well so it does not start moving and/or deforming later.

As for the concrete - High quality concrete with local materials should be fine.  Normally slabs use 2000-2500 psi concrete.  It has the strength you need, but is likely to crack.  The 3000-3500 psi mix will allow you to avoid joints altogether.  Reinforce the slab with steel bars that are placed at the center of the slab.  This is very important because too often the steel ends up at the bottom where it is useless.  The bar spacing depends on other parameters but should probably be between 10-12 inches apart.  The contractor should be able to use his experience for that.

Another critical thing is the curing method.  If not cured properly, even the best concrete will fail.

In your case I would recommend sealing the surface with curing compound, AND misting the concrete for as long as possible.  The purpose is to keep it from drying before it gained enough strength to withstand the cracking stress.  Three days of moist curing is nice; 7 days is good; more than that will only result in marginal improvement.  Use a misting nozzle at first (start 3-4 hours after they finish work) that will not harm the surface.  The next day you can simply "flood" it with water.  Cover with plastic between watering and protect it from excessive heat.  If it is placed during a hot dry day you may have to accelerate the curing start since heat will also accelerate the concrete hardening and drying.  The contractor should be able to tell when it is safe to start misting.

I am not familiar with contractors in your area.  Check the yellow pages; some of the construction related sites; or walk around the area and ask people who built their courts...

Get the contractor's license number and verify that it is current.  Make sure he is insured (performance bond and workman's comp.).  Check the BBB for complaints.  Get references and check them out!  Make sure he obtains the needed permits.  Retain a testing laboratory to sample and test the concrete (this is a little more than most people do and you may not wish to spend the extra couple hundred dollars...).  And do not pay in advance!  In California, by law, a contractor cannot ask for more than 10%.  Most of them will do anyway, but you should not pay them.  If he cannot wait for the payment, there may be something fishy in his operation.

Hold back at least 25% for a week after completion.  At that time go over the concrete very carefully and look for any cracks or deformations.  Make him repair or replace before final payments. 

I could go on forever about precautions with contractors - but maybe you will find the "good" one and have a pleasant experience.

Good luck.