for my wag (wild as* guess), I would go with a wiring problem to the coil, (like combar said) or the coil itself, and if that is not it, then (like simon_k said) the suction hose from the carb to the regulator.
change the hose that the fuel travels to the carb in, change the diaphragm in the carb (unless, as you say, you know the carb is good by installing it on a known good unit,) and run a jumper straight to the coil from battery positive. this may well even just be the contact for the "run" position inside the key switch, or the wire on the back of the key switch, either run or battery positive being just a little loose....