Are they big enough? If the hard draining surface is already there I'd have a look/ chat to someone like the flexiride stuff that you can put straight onto concrete without sand.
We looked into this. There were a couple of problems, the tennis court is too small for 20x40 and would need to be extended and the surface is not flat which is not ideal for an arena. The money that would be required for the conversion would be best spent on a proper arena.
Oh if you were to do it anyway don't put down the membrane it would be lethaly slippery on the tennis court. The membrane is there to stop stones from coming up and sand from going down, neither of which is going to happen with a tennis court surface!
We have one at the yard, a little smaller than 20x40...set on a mound so ideal really....except the drainage...it is awful - been flooded since beginning of December...I don't realy know how it was put in, it was 10 years or more ago, so perhaps they didnt do something right then, but they have had to have holes drilled through concrete and gravel poured in to help...it hasn't solved it...perhaps it is the surface that is now useless - it is sand and rubber - so to be fair I don't know that it is because it was a tennis court or because of surface not good after so long - I should think you would be best off still digging up concrete and starting like any other menage to help drainage.
It wouldn't drain properly. You could use the surface of the court as some of the materials for the school but it would have to be dug up and put through a crushing/screening machine before being put down again.
You would need to dig up the entire tennis court and the rubble/hardcore below it and start from scratch if you want it to ride well and last .
If you want a decent level, long lasting arena/manage then you will need to spend some serious money and use specialist contractors (look at other manages/arenas that they have built and talk to the people that ride in them.
A well built manage is a little like a multiple layer sandwich and will consist of several different layers which are drainage/membrane/rubble/membrane/surface and of course good quality fencing.
Think you would need to do some work on the surface of the tennis court as it could create a very slippery surface if not prepared correctly and like others have said would also not drain.
Friend has one, about a 6 inch layer of woodchip and makes a lovely lunge pen (Is quite old so some of the woodchip has rotted down to make a more secure base now) - Not sure what it was like when 1st put in. but now - cracking. Drain's a treat!