One doesn’t give up rights as a citizen by becoming a Supreme Court justice. What if a drunk driver crashed into a Supreme Court justice’s car and crippled him or her? The justice would certainly be able to sue for damages. A defamation suit would be no different. If the case ever made it to the Supreme Court, such justice would be recused from the case, of course. I’m sure Supreme Court justices have been parties in private legal matters before, but haven’t taken the time to research specifics.
It just seems like a scenario that's too bizarre to even contemplate.