Is there a way that I can set the time capsule up to back up while my computer is asleep
I set up the time machine and I find that it is taking 6+ hours to back up and I was wondering if there was a way to set it up but keep the computer asleep.
6+ hours would not be all that unusual if you are making the first "master" backup of your Mac. But, once you have the first backup completed, subsequent or incremental backups should only take a few minutes each hour.
If you are saying that regular daily backups are taking 6+ hours, then something is very wrong with Time Machine, as it sounds like it may be backing up your entire cmputer each time that it runs, and not just the changes that have occurred since the last backup.
As far as whether your Mac will back up while it is sleeping......see this Apple support document: