Making Time Machine Backups while Mac is in Sleep Mode
You can schedule your Mac to wake from sleep or boot at a specific time. Go to System Preferences, then the Energy Saver pane. In there, at the bottom-right, is a "Schedule…" button. Pressing it brings up a sheet where you can set a day and time to wake up and another to go to sleep. If you leave a half-hour or so between the wake up and sleep times, it should have enough time to back up.

I must say, there's not much point in running a Time Machine backup when you haven't been using the computer: if you're not using it, nothing has changed, so there's nothing new to back up. I should also note that if the computer is shut down (like if you're on vacation) it'll boot and then go to sleep if you don't turn the schedule off before you leave.