I have a 2002 cavalier 2.2 when I start it up the motor shakes bad and its not a motor mount and black smokes comes out of exhaust I've been told tension pulley o2 sensor I was thinking maybe it jump time any ideas

Black smoke is usually an indication of unburnt fuel. I would check all of your ignition components. Pull at your spark plugs after you run it for a minute and see which if not all is wet and black with fuel. That would be were i would start. And it should help lead yoy to the culprit wether it be a bad could pack or ignition module, plugs or what have you.