Chat with registered users based on Online/Offline status

I am running on B2B website and I want to integrate chat messenger for registered users chat with each other privately based on user’s online status once he/she logged in.

I have tried some modules like Drupal Chat, Mylive Chat, etc and these are all for public chat. I found private message is nice but its not related to live chat.

Is there any other way to achieve this?

Drupal version: