imarkelis

Ok. I got it. The only thing I had to do was use the object itself by refering to it ($this). So I changed the code and voila. No need for a static function.

public function couponsgen_add_dashboard_widget() {
            //$cg_widget = new Couponsgen_Admin();
            //$cg_widget->couponsgen_create_dashboard_widget();
            wp_add_dashboard_widget(
                'couponsgen_dashboard_widget',
                'Coupons Generator Dashboard Widget',
                array($this, 'couponsgen_create_dashboard_widget')
            );
        }

Thank you very much for the quick response!

I also had to turn my function to static cause I got the message

Strict standards: call_user_func() expects parameter 1 to be a valid callback, non-static method

The final code for adding the widget is

public function couponsgen_add_dashboard_widget() {
            wp_add_dashboard_widget(
                'couponsgen_dashboard_widget',
                'Coupons Generator Dashboard Widget',
                array(__CLASS__,'couponsgen_create_dashboard_widget')
            );
        }

and for putting content inside the widget is

public static function couponsgen_create_dashboard_widget() {
           echo "<p>Hello World! This is my couponsgen Dashboard Widget</p>";
        }

Thank you very much for your help!