Should I tell a joke my friend doesn't want me to?
What did your friend tell you that was private?
I think I'm going to tell a joke about how he gets nervous about his relationship.
Your friend shared his issue with relationship anxiety in confidence, and you making a joke about it in front of others defiles his wish for the information to remain private. Keep your friends secrets or be prepared for people to see you as untrustworthy.
My friend said that nothing was private.
You should get your story straight and make sure what information your friend doesn't and does mind if you share. You wouldn't want to embarrass your friend, so try not to say anything rash about them.