What system should I implement to make use of accounts with Bitcoin Core 'accounts' now deprecated? I am designing one of the Bitcoin based app on Bitcoin-Core using account system. 

Accounts I have used to store users wallet balance in different accounts. 

But since I know it is deprecated, then how can i store users individual balance in separate identifiable addresses.

Is there any database we need to implement?
Accounts were replaced by labels, a more flexible tool which can probably be made to fit your requirement. Alternatively, if you have really been using the now-obsolete "accounts" feature to maintain separate wallets within a wallet, there is now an option to use separate wallets in separate wallet files