When using the nuvaring is it common to get brown discharge?

Probably blood: Brown discharge is usually old blood. About a third of women using birth control will experience breakthrough bleeding (bleeding at the wrong time). This usually resolves on its own and does not mean something is wrong.

Brown old blood: The brown discharge may be old blood from either the uterus or more likely the Nuva ring when it abrades the vaginal walls during sexual interaction episodes.