Engine Cooling problem
2003 Chevy Impala 6 cyl Front Wheel Drive Automatic
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Help please have already spent over 1000.00 on repairs .The car started turning off a week a ago to it to pep boys they replaced the spark plugs ,spark plug wires,did a cooloant kit,diagnostics, replaced battery . it worked for about a week the yesterday it brokr down again it shut off it was over heating took it back to pep boys they could not figure out what was wrong finally the master tech suspected that the MAP was clogged and need replacement so i had them replace that it turned on for a while and then it shut down still over heating so they say they have no clue what is wrong but suggest that it may be the catalist converter,electrical,fan housing,wiring they are still working on it and cant find a solution to the problems oh yeah after they installed they MAP sensor the car start emiting balack smoke....
So i could really use some advice if u need to contact me call me at 2109950618

The black smoke is likely due to a rich fuel/air mixture (too much gas is burned).

You could have a leaky fuel injector, a defective fuel pressure regulator, a clogged air filter, a problem with the MAP sensor, a defective coolant sensor, a defective o2 sensor, TPS sensor, problem in the EGR system.
You could also have more serious internal engine problems (like burnt exhaust valves).

First thing I would do: hook up an autoscanner to your PCM and check for DTCs/pending DTCs. Make sure the readings from all the sensors are within range.

Honestly, I'd be very careful with a car shop that starts replacing one part after another without doing any real diagnostic.
I suggest you take it to a different car shop (one recommended by a friend or something).

Given your description of the problem, a glogged catalytic converter could be the culprit indeed; however it could be many other things as well. (check intake vacuum at idle; if low and keep dropping check your exhaust system).
If it turns out to be the converter, I recommend you replace (or at least inspect carefully) your O2 sensors. They are very important for proper operation of the catalytic converter.

If the converter is alright and the sensors test fine, I would probably take a look at the charging system (if you have a problem in your charging system, it would eventually result in your car turning off).
When your car turned off, were you able to start it right back up, or did you have to jump start it?

Also, do a fuel pressure test; it should tell you if there's any problem with your fuel system.

Check for vacuum leaks. It could cause your car to run roughly or stall. This should be more noticeable at idle, thus my following questions:

does your car turn off at idle or when you're driving?

Finally, if you still haven't found the problem, do a compression test; it will tell you if you have internal engine problems.