I got my rabbit from the animal shelter a long time ago, and whenever we went there, we went to go look at the dogs also, and they all stare at you, and begin to cry. Whenever we went to look at the rabbits, they all look up at you, but I am wondering if rabbits can also cry?
Rabbits do have tear ducts that keep their eyes lubricated, but any excess tears would be an indication of a medical problem. Infection, allergy, trauma to the eye, or a blocked duct can lead to excessive tears.
The references below, attest to this, but a better example in this case may be first person event. When Ruby was sick with botulism she never shed a tear. She was voicing anger (thumping) she was also presumably very scared and sad. Over the course of a few hours, she went from perfect to full body paralysis (quadriplegic). During this she was closely attended to, and watched for any possible sign or symptom. There was no sign of crying.
Ruby is a cuddle bunny, she enjoys getting petted, snuggling and she chatters her teeth (bunny purrs) in appreciation. During her illness she was more vocal in her chattering, the assumption I make her is that it was an emotionally difficult time for her, and she was extra appreciative of positive attention.
Lyra who died from the botulism, spent her last minutes with me and also had no sign of tears.
When rabbits are in extreme distress (fear or pain) they will scream. This is a not a sound you ever want to hear, I heard it once twenty plus years ago and it still bothers me.
So in answer to your question, a rabbit will only shed tears when they are sad and/or suffering if there is something medically wrong with their eye at the same time.