I always thought that the Dornier 328-300 was not certified for LCY because Sun Air always used leased in MHS turboprops on the BLL/HAM-services. But apparently the jets were certified in 2011.
As I understand it, not only does the type need to be generically certified for LCY, but the crews need to be individually as well. Thus although Sun-Air has had Do328 Jets for some time, their jet crews may well not have trained to have the certification. I think that ever since they started into LCY they have used German-registered and operated Do328 Prop aircraft.
Over on the BA page here there's a discussion about Sun-Air being about to base 2 x Do328 Jets at Bremen from September, one of the new routes from there being to LCY.