I find picky bunnies are more inclined to eat aromatic greens, such as herbs. You can try dill, cilantro, parsley, basil, etc. One of my bunnies is very picky-she doesn’t eat much and she won’t try anything new. Once she tries something, she will often eat it, so I try offering a vegetable many times even if it is refused. Another sneaky trick you might try is tickling your bunny’s nose with a piece of herb/vegatable-sometimes that will irritate them just enough that they will bite it (and try it!).
Usually, I give my bunnies lettuce, cilantro, kale, and spring greens, as well as occasional pieces of banana and apple.