No laughing here, lots of people use Godaddy. I do not particularly like them for hosting but I have about most of my domains registered with them.
At any rate I believe you can set up a cron task()scheduled task) using their back up system and set it to keep only 1 or 2 back ups. I cannot recall though if this is built in or part of the managed back up service they offer. You could always opt for that.
http://support.godaddy.com/help/arti...anaged-backups
I do not even know though if you have a VPS, shared or dedicated plan.