$ sudo vi /etc/logrotate.d/rails_production
/var/log/co-meeting/production.log
{
    rotate 7
    daily
    missingok
    notifempty
    delaycompress
    compress
}

動作確認

 logrotate -dv /etc/logrotate.d/rails_production
reading config file /etc/logrotate.d/rails_production
reading config info for /var/log/co-meeting/production.log


Handling 1 logs

rotating pattern: /var/log/co-meeting/production.log
 after 1 days (7 rotations)
empty log files are not rotated, old logs are removed
considering log /var/log/co-meeting/production.log
  log does not need rotating

参照 Redmine.JP production.logのローテート