Stephenie Meyer has put a lot of thought into that. Acording to her the body chemistry of Vampires is basically a series of venoms that arent infectious like the saliva venom. The function of tears is to protect the eye from foreign bodies, and because nothing can harm a vampires granite hard eyes, they have no perpose for tears. No, they cannot cry. As they can't show any emotion.But as Bella and Esmee show they can cry in a way it feels like the air gets stuck in their throat but they don't shed tears.