What you are talking about, is training for functionality. If being balanced in the air is your goal, you must train in the air, ie plyos and practicing your layups.
You can start with low level plyos, like squat jumps, box runs, and explosive step ups. This will strengthen the connective tissue and help you develop a "base" for your plyometric training.
Also, heavy weight lifitng will help you in your goals. If you have more muscle on your body, you will absorb blows much more easily. Also, heavy training helps to strengthen connective tissue which aids in durability.
On a side note, I never used a stability ball up until about a year ago. Within a week of practicing, I was able to stand and squat on the ball. I'm 6'2 and approximately 240lbs, and I have a coordination disability.