Automate cpanel website & database backup

I would like a way to have automated backups of each website I host. I run the websites on a shared hosting with Apache so I don't have access to install anything on the server, only the root of each site. I would like the script to run using cron jobs and I would like to backup the public_html folder as well as perhaps any mysql database (optional and perhaps not required). Additional features would send the backup to another server. The script should be very secure and not accessible over the web.