My grandma lived in SE New Mexico and she had a Lila tree in her front yard (sorry I don't know the name in English or even if that is how it is spelled). We used to always get in lila fights with our cousins when we went to visit. They weren't good for much else--hard little cranberry sized fruit, always green. Left a nice welt if you threw it hard enough.
It sounds like a China berrytree. My grandmother always cautioned us that we were going to DIE if we ate the berries.