[St. Lou Stu]

Timing belts usually do jump when the vehicle is shut off or goes to idle after acceleration.
That said, they typically don't over fuel as a side effect of bad timing. The black smoke is a clear sign of too much fuel.
Pull the plugs. Are they all black or darker than usual? Or just one?
If they're all darker than normal, it is a general problem affecting all cylinders.
I'm not familiar with that particular vehicle, but I would start by checking the air temp sensors and coolant temp sensors. Also, if it mas a MAP (Manifold Absolute Pressure) or MAF (Mass Air Flow) sensor, check it for proper operation... Usually, you will have one or the other, not both.

Back to pulling the plugs. Which one is black if they all aren't? If just one is odd looking, you can narrow it to a single cylinder. If that is the case, look at plugs, wires, coil, injector for the affected cylinder.

This is a hard to diagnose remotely kinda problem.

All that said, timing may still be the culprit. That should be easy to check.
You should be able to pull the valve cover or timing belt cover, whichever yuor car has that covers the cam gear/sprocket.
Rotate the crank pulley to top dead center (there should be a mark (dot, arrow, line...) on it. Look at the cam sprocket/pulley is it's mark also top dead center? If not, rotate the crank 360 degrees and look again. The Cam should now have its mark at TDC. If it isn't, you gots a problem.