I agree with Oldvart. The Carter AFB is one of the most trouble free carbs ever built. It's just like anything. When it don't work right and you don't know how to fix it they can be a real headache. Don't ditch it just cause of that. The next one maybe just as bad, Or worse.
340Demon had a good point about the little check ball. It's so small it can be overlooked and left out easily. To find out if the accellerator pump circuit is working properly all you need to do is take off the air cleaner and look down the throat of the carb. (with the engine shut off) and pump the accellerator and you should see a double stream of fuel spray from the front center of the carb. If you don't see this happening this is where your problem lies cause if the accellerator pump circuit isn't working it will stumble and stall just like you've described. LOL