Like Vikki said, some testing and clarification of the problem is in order. That will point to the solution. At first glance, I'd say it is a fuel delivery issue but the info so far isn't sufficient to rule out the fuel pump or maybe ignition or possibly several circuits in the carb that need addressing.

Backfiring is almost always caused by a lean condition unless there is so much fuel that raw fuel gets into the exhaust and then is ignited when the cylinder refires.

The soot may be caused by excess fuel in another circuit of the carb. Richening up the idle mixture screw adjustment in an attempt to compensate for a bad or nonexistent accelerator pump shot, or richening up the main jets when the fuel pump is at fault are examples of chasing the wrong things to fix the problem.

Have someone follow you (if they can!) while you test each phase of the carb to see if you get black smoke at any time. If you don't have smoke when the problem arises, you are having a lean spot. Either way, figure out what circuit(s) in the carb is/are working when the problem shows up or post the results and we'll all pitch in!

If you need a few ideas on how to test any part of the carb function just ask.