docker run -d -p 514:514 -p 514:514/udp -v /var/log/remote/:/var/log/remote:z centos7_rsyslogd_container

• /var/log/remote = directory where the logs will be stored
• :z = set SELINUX label
• 514/udp = the port that rsyslog will listen on

Add rsyslogd config file to this dir, and they will be copied to /etc/rsyslog.d in the container..

I have included a systemd-unit file, which can be placed in /etc/systemd/system so that the service will start on boot (if enabled with systemctl enable..), or you can use it as a template. This systemd-unit file in particular will always restart the container if it stops.