Hi,
As you mentioned that you will be taking different backups in the night time targeting them on the slots of Tape device.
Now you want to duplicate all these backups that were run on the previous night.
You can duplicate the existing backup sets (on the next day morning) that ran on the last night.
It is not possible however to schedule this duplicate job.
You can refer the Backup exec admin guide manual, page no # 307 onwards,
You can download the soft copy of the manual from the following link,
http://seer.support.veritas.com/docs/266190.htm