Plastic is just like most surfaces, it requires the correct primer before you can paint it. If it is really shiny I would recommend that you sand it down a bit to dull the sheen. Go to your local paint store or big box and get a primer recommended for plastic, then paint with a good quality latex based paint.
I just put up new garage steel doors with plastic trim. I followed the directions the garage door people gave me. First wash the plastic with soap and water and let dry. Then,and I used a spray can, of primer made for plastic. When dry paint with water based paint of your choice. I also masked the area around the plastic so I would not get any plastic primer on the steel doors.