As a tennis player recovering from tendinitis, what kinds of vitamin supplements should I be taking?

No specific vitamins. For a healing tendon, there are no specific vitamins needed to aid in the healing. This is assuming that one eats a balanced diet with lean proteins, plenty of fruits and vegetables, and low saturated fat. If one does not eat this way, a plain multivitamin can supplement (but not replace) a proper diet.
Intenzyme. Intenzyme, wobenzyme, bromelain, cats claw are few meds that help inflammation. For faster healing nucleotides helps.