My 1963 Ford Thunderbird has black smoke coming out of the tailpipes
Too much fuel. Check for a sticking choke OR flooding caburetor.
Running rich, for what ever reason. Noted about are two. The third main culprit is the idle mixture set too rich. Most people seem to do that, and all it does is waste gas. It is a simple fix, though. Start on the passenger side, and turn the mixture screw in until the idle slows a touch. Then turn the screw out until the idle is as high as it goes. Then turn it about 1/8 turn more. Repeat on the driver's side mixture screw. Put the air filter housing back on. You may well have to lower the idle, but use the adjustment at the throttle linkage, NOT the mixture screws. That is how so many carbureted cars end up running rich.
Search Ford Thunderbird Questions
Are you a UK consumer? CarGurus now has a discussion forum in the UK.
Ford Thunderbird Experts