Which type of eye related transplant can be done in which the donor is still alive?

Few if any: The only possible tissue that can be transplanted while the donor is alive would be small amounts of skin from the eye's surface if there was a genetic match. Unfortunately, the small amount of tissue available and the high risks of graft rejection make this type of transplant impractical. Corneas, which are a relatively low rejection-causing tissue, can only be donated after death.

None: The cornea is the only part of the eye that is transplanted. Corneas are only recovered from deceased donors - not from living donors.