what are the conditions of old spark plugs? Are both light grey or one is darker?
In this case,maibe one ignition line has gone...
If you are quite skilled in mechanical handwork you can try to solve yourself the trouble, otherwise, go looking for a good dealer!
IGNITION DEBUGGING...
start the engine and pull the ORANGE WIRE off one coil and listern to the engine: if it falls down or dies the cylinder is working.
Repeat with the other one: If both the cylinders work good you might have to search somewhere else your trouble.
If one cylinder does not work good, try to excange the ignition boxes (engine off!) and repeat the operation.
If the cylinder not working is still the same, both ignition boxes run good.
try to excange the low voltage wires on the coils (maybe brown and green? I'm not sure about the color, anyway the other "non-orange" wires on the coils) and excange the hi-voltage wires to the spark plugs too.
This is to excange the coils without remove them. If the trouble don't change, this might not be an ignition bug.
WEBER IDLE CARB DEBUGGING
Remove all fairings and fuel tank, and arrange a fuel supply
Look for the idle jets in both sides of the carburateur
they look like a bronze screw just over the main axle. Start the engine.
Unscrew one of them just 1/2 turn and listern to the engine... If it runs higher, you found your bug: grain of dust in the jet, remove it and spray air in the inner duct.
This might be the right chance to have a look to the carb setup
Have a nice work, and