theorically they can't because vampire's body is composed Von marble and it can't change...they are Frozen in the moment of transformation for ever even if they can feel emotions :)
Vampire are unable to shed tears, because that involves a bodily function. A vampire's body doesn't function like a human being's does.
Example: When Bella discovered that Jacob told Charlie about his being a werewolf, Renesmee, and Bella being fine...she stated that she was crying with tears she couldn't shed.
Vampire hybrids (Renesmee, Nahuel) however, are able to cry.
No. In Breaking Dawn when Bella's thinking of the threat from the Volturi, she states that she has this burning sensation in the corners of her eyes, instead of crying, because the venom has solidified her tears.