Of course I don't want to implement a cloud backup here.
Why not?
What is the best way to
locallyand securely backup the data of passwords only so that upon reinstalling the app and logging back in the data since backed up , it won't be lost.
Cloud backup.
While an app can store stuff in a dataset in shared storage (see Ewan's answer), I'm not sure it's a good idea to use that for the backups, for two reasons:
Things happen: apps get uninstalled and devices get lost, stolen or broken. And when somebody gets his smartphone stolen, the last thing he needs is an additional headache about all his passwords being definitively lost.
If you discuss with your users, there is a strong chance that they would want not just a backup, but background synchronization. Essentially, ofIf I create a password on my tablet, I am expecting to see it on my smartphone as well, automatically.