There are three reasons that you would have a puff of black smoke when you hit the throttle.
1) The EGR is sticking open a bit. The throttle will lag, then suddenly, BOOM! you have a power surge, which can smoke. Clean the EGR valve. Less likely...
2) You have a Turbo Actuator rod that is closing too much. When you hit the throttle, the actuator wants to open the VNT on your turbo, but the the vanes that are closed too much, and the exhaust pressure keeps the vanes closed...It smokes and belches. Let the pedal off, then back on, it passes the crisis and the vanes open correctly. There is a goofy wire lasso we make to correct that problem. Somewhat likely...
3) Your cam is worn out. Remove the valve cover and look for the tell-tale signs of galling on the base circle of the cam. If you see this adverse wear, and also, the tops of the lobes have sharp edges, especially on the exhaust lobes (1, 3, 6 and 8), you have a worn cam. Because of the reduced lift of the cam, not enough boost pressure comes in with the associated fuel charge. This causes the first few seconds of engine revving to puff black smoke. Very likely....
In CA, they want to eliminate diesels. We do have a cam kit, if you like. The other 'fixes' are just a matter of know-how.
Let us know if we can be any additional help.