The Konigsberg is a fantastic ship that requires both patience and daring to do well.
If you have the patience to hang back (just a little) at the beginning of the game, and use your concealment, maneuverability, and the map to your advantage, you can contribute with HE vs dds.
Later in the game, use AP to surprise enemy cruisers who show broadside, and torpedos on BBs. Engage, disengage, kite...stay alive and KEEP SHOOTING.
I have to say, it is my favourite ship. The challenge of so often being low-tier just adds to the satisfaction of scoring hits and kills on higher-tier ship. The bonus XP is nice, too.
I regularly do over 50k damage (double the ship's hp), and sometimes over 70k. Of course, you WILL be deleted by one BB salvo now and again, but that can happen in just about any cruiser when you have exposed yourself and the enemy team sees your mistake before you can correct it.
If nothing else, the Konigsberg is a great ship to build map awareness. Recommended! :^)