You would get a sharper photo at f8 than at f5.6, so try stopping down a bit. I'm not sure what the sharpest aperture is at 200mm on this lens, but f8 will give you a sharper photo. You could up the ISO to 400 or even 800 to maintain or increase shutter speed.
How are you firing the shutter? If you're pressing the shutter release on the camera, that could induce some movement in the camera.
Because the 18-200 is not at its sharpest at 200mm, if you're getting sharper photos from your D80, it might be that the higher pixel count in the D7000 is revealing the limitations of the lens. But experiment with f8 or higher and see if you notice an improvement.