As CT said, try and push your shutter speed up. If using a DSLR this is easier as you can just increase the ISO for a particular shot. Try and keep it at 1/250 or faster when at 200mm and you should be ok, depending on how much coffee you drink etc. If you're already pushing the sensitivity as far as you can/like then opening up the lens a stop will halve the shutter speed you require.
In shutter priority try setting to 1/250 or 1/500 and see if that helps
Other than that a tripod or monopod is the way forward.
Hope that helped?
Col