piaggio x9 250 lumping?

running better without the air filter indicates its trying to run on a rich mixture, the plug will be very sooty, think yours is a Honda type CV carb with a rubber diaphragm carb slide, the slide could be sticking in the lower position check by removing air filter and pushing with a finger slide all the way up should slide very smoothly up and it should drop down on its own. Or idle jet blocked, remove carb then remove float bowl unscrew idle jet from under carb body (very small screw next to main jet) blow through with air or carb cleaner spray. Or it could be the float is leaky and has fuel in it you can hear it by shaking or see it through a clear plastic type, check float needle's not sticking in its seat.

Grizwold
March 2016