The BBSs of the 80s had the concept of the Twit Bit, which, if set for a user, they were the only ones who would see their posts. It was if everyone else were simply ignoring their posts.
Another approach was selective downtime: have the modem accidentally drop the connection when the problem user dials in, say, 50% of the time, in hopes that they'll get too frustrated to keep connecting, but without getting angry enough to plot revenge (because hopefully they'll think it's just an unreliable system).