I implemented the TLSSyslogAppender, which is capable of sending syslog messages over TLS. It supports the old legacy BSD and the new RFC 5424 syslog format, too. I haven't written tha javadoc yet, because I'm waiting for feedback from you. I would appreciate it if it would become a part of logback. You can find the git repository here:

https://github.com/balabit/logback/tree/tls-syslog-appender