1986 Chrysler Fifth Avenue, running rough and black smoke from tailpipe

I think you should just sell this car. Oh, and I'd be willing to take it off your hands although I really always wanted a dark red one!

Based on age and mileage, I'd start with the basics, spark plugs, wires, distributor cap and rotor. Next, check for an EGR valve stuck open, often due to a chip of carbon stuck in the valve. You can unbolt it and slide a thin sheet metal shim under it to block the ports as a test.

The instant you stop the engine, look down the inside of the carburetor to see if fuel is still dribbling in. If it is, there is dirt in the needle and seat preventing it from closing. Unlike fuel injected cars, there isn't much that can cause a carbureted one to get too much fuel.

You can also try pinching the rubber hose feeding the fuel pump. If the engine clears up, suspect the needle and seat again. It will run on the remaining fuel in the float bowl for about a minute. Incorrect float height will cause that too but that isn't going to change on its own. Since it ran fine a few days ago, you know the float height is okay.

That looks more like carbon being washed out of the exhaust system by water. Black smoke from running too rich will leave the tail pipe too but that will float away. Too much fuel won't leave anything on the ground.

I have a '93 Dynasty with only 4,100 miles and it has always done the same thing. One of the byproducts of a properly working catalytic converter is water vapor. That's why there is usually a small drain hole at the back of the muffler, on the bottom. Since yours is higher mileage, what you might try is to get the engine up to normal temperature, then spray some water into the carb while the engine is idling. Don't get carried away with pouring it in. A mist from a spray bottle works well. The cool liquid will shock the carbon in the cylinder heads and valves and will help it break off. That water will also slow down the combustion and make it more even vs. A rapid "bang-and-it's-over-with". That is why engines seem to run so smoothly when you're driving in the rain.

Carbon buildup seems to be much less of a problem than many years ago, but who knows what happened with the previous owner. I CAN share that a former instructor had a regular customer who had a running problem about twice per year. He had it figured out that each time that car showed up, he took it out on the highway and started out at around 30 mph and stomped it to the floor for about five seconds. The engine ran fine after blowing out the rust and spider webs. Now, that was back in the mid '70s but still worth considering.

Another thing you might think about, since you mentioned the "putt-putt", is a burned valve. This too goes back to the '70s and affected a '78 LeBaron I still have sitting in my yard. The problem was mostly a problem of leaded gas going away. That lead acted as a lubricant and softened the valves landing on the seats. Some people said it was due to lower quality metals being used for the valve seats but it wasn't the seats that burned away; it was the valves.

The offending valve was one of the two middle ones on the passenger side. When cold, the heat-riser valve in the right exhaust manifold closes and the blocked exhaust from all four cylinders has to go through that one port, through a passage in the intake manifold to warm the base of the carburetor and choke thermostatic spring, then out the left side. That increased flow through that one sad passage might be a contributing factor to the burned valve but that only occurs for about five minutes when the engine is first started and is still cold. I can't say for sure if that's the causes of the burned valve but it does always seem to be the same one that is affected.

I am fairly certain the problem was addressed by 1986. Still, since you're hearing that sound at the tail pipe, you might want to consider performing a cylinder leakage test. Check the auto parts stores that rent or borrow tools to see if they have a tester. It involves pumping regulated compressed air into each cylinder, one at a time, when the piston is at top dead center on the compression stroke. To make it easy, there is a whistle you can hook to the tester's hose to tell you when the piston is coming up on the compression stroke. When it stops whistling, you're there. The gauge on the tester shows the percent of leakage, and you can listen in four places for the results of that leakage. If the exhaust valve is leaking you will hear hissing at the tail pipe.