Oeh, that's tough. You should try planches and handstands mainly. Try starting with help from a partner or something you can lean against and gradually work up to using no external stabilization. Balance is key.
Planches: You also want to have a REALLY strong core and posterior chain, so glute bridges and deadlifts are your friends. Do plank variations and reverse hyperextensions too. Try doing those exercises (not the deadlifts though!) on unstable surfaces to increase balance.
Handstand: Start with handstands against a wall and work up to using no wall. Standing DB Military Presses will help, but this exercise is all about balance, even moreso than the planche. Core training is vital as well.
A strong grip will also help a bunch.
Finally, you want to do a lot of isometric work, especially for your core. The key to success in those movements is preventing movement, not causing it. Don't waste your time on endless sets of crunches. Reverse hyperextension holds, hyperextension holds, planks and roll-outs are far more beneficial.
All in all though, your weight training program won't differ that much from that of the regular gym rat. You'll want to have a balanced program too and what you do in the gym is general stuff. Your athletic training session, aside from your weight training, will be centered on the specific exercises you mentioned: working on technique and balance.
Suggested reading: functional training for sports by Michael Boyle.
Good luck.