How to restore no longer available app from iCloud Backup
Did you ever sync or backup to iTunes? If you could restore from backup from iTunes that wouldn't be a problem, but short of that you could still see if it has the app you could copy to your phone. Not sure if that would include the documents and data though.

If by any chance that app syncs over iCloud or some other cloud service, the raw files may still be accessible (but still likely encrypted).

I personally would contact the app developers and see if they have any ideas.