Engines that play Mangala?
I'm not sure if this is what you're looking for, but the name is correct. Here is Mangala game available on the AppStore. I haven't played it, so I can't confirm that it's using Turkish variant of the rules rather than the most popular one from Mancala.

I guess we have to wait until you introduce a playable game of Mangala! :) Of course if that's what your project is about.

You could specify in your question (list) what rules are important to you to be included in the version you're looking for. Take a look here, maybe one of those games is similar enough.