An option should be there to lock messages from a specific person with a password. Please don't add any private box like other messaging apps. There should be an option to lock conversation of a specific person so that when we want to open that conversation from conversation list, we have to input password. And messages from that person should appear in notifications like this " The conversation is encrypted ".
This option should be only in-app and not system wide, I mean other messaging apps may be able to read and render encrypted messages.
I have such an app which was stock messaging app in one of my android mobile phones. I can send you that if you want to have a look.