have you created a script that will backup the directory to the destination you desire in the way you want to back it up? if so then as user you can create a crontab -e (the -e = edit) and put in something like this:
0 21 * * * /path/to/script
that would run nightly at 9pm local.
you might have to give the user permissions to run its own cronjob by adding the user name to /etc/cron.allow or were ever that file is located on your distro.
what gdejonge said about rsync is great, but keep in mind that has to be run as root. if you just want to cp, not as clean as rsync mind you, or tar the directory to save space then user rights are just fine.