If application data is kept in a particular part of the file system, you might decide to perform regular backups of this data only. The zone's root file system might not have to be backed up as often because it changes less frequently.
You will have to determine where the application places its files. Locations where files can be stored include the following:
Users' home directories
/etc for configuration data files
Assuming the application administrator knows where the data is stored, it might be possible to create a system in which a per-zone writable directory is made available to each zone. Each zone can then store its own backups, and the global administrator or user granted the appropriate authorizations can make this location one of the places on the system to back up.