There have been a number of suggestions for quicker, easier diagnostic procedures that will find the issue than testing the compression. Seriously, you could have tried all of the suggestions offered in less time than it took to run a compression test. No way could a compression issue cause the problem you describe, hence the reason nobody suggested it.
I realize you're not that experienced with this stuff, but you've been given some great ideas here, none of which cost more than a few bucks to check. You keep asking but you haven't apparently tried anything yet. The car ain't gonna fix itself while you're discussing the problem.
The black smoke is new; it should've been mentioned in the first post. It sounds like overfueling (running way too rich). That leads me to believe that "we took to a shop and rebuilt it,"--I assume means the carburetor--didn't work out so well. It sounds like the carb is leaking fuel directly into the intake. With the car ice cold, back the idle screw out far enough that it's no longer touching the throttle lever at all. Pump the carb once to set the choke, and run the engine up to temperature. Just when it sounds like it's ready to stall, throttle it swiftly with your hand and make sure it drops off high idle. Let the car stall, then look down the carburetor throat. If you see fuel on the butterflies, it's time to rebuild the carburetor (again?).
Do NOT go into a parts store and tell them you need a carb kit for an '87 anything. Give them the carburetor brand and the number off the carb and no other information. The carb number (called the "list number") should be stamped into the carb, or look for a metal tag under one of the screws. "I need a rebuild kit for a [carb brand], number [carb number]" should be all you tell them. Simply put, unless you bought this car new, you have no idea if the carb was changed at some point. They're not "all the same", as carburetors changed from year to year, and often between the same engine in different models. If they can't find a rebuild kit by carburetor make and list number, find a different parts store! Don't fall back on "Well, it's an '87 Plymouth Gran Fury..." since it seems that didn't work the first time.
I worked in parts for nearly 30 years. I refused to look up carburetor parts by vehicle application. I told them to get me a carb number every time, because carburetor kits are not returnable if opened--and the customer has to open it to find out he got the wrong item. Some carb kits can cost over $100, and nobody wants to eat that mistake.
