How to show every second user different types of banners?

Instead of using the Options API, you’d be better off using the Transients API, however in either case you’ll be polluting the *_options table (even if you use transients with expiration times).

I’d possibly recommend using wp-session-manager plugin by EAMann’s which will allow you to use and store $_SESSION data in a dedicated sessions database table that the plugin creates upon activation (or where it does not exist).

Reading:

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)