Quit running 2008 Gilera Runner SP 50

Your coil problem, change with the new one.

First check your main fuse, then check the fuse in the starter relay.

could be weak battery or bad terminals, on the solonoid cross the 2 bolts, careful it will spak does that turn the starter, if so then its a corroded connect check all connections remebering the battery earth to engine. to check battery your need a volt meter, it should read 12.8v or more any less and the solenoid will just click

coil lead plug cap needs replacing , no shield to protect spark plug from getting wet due to weather/water splash. electrical spray lubricant requires from damp start problem

Any Gilera 50 scooter carb will do

A good rule of thumb is they have to be over 100psi to start and run. I have found they can be up to 170psi on pump gas.

Sounds like your oil/ fuel mixing valve may need to be replaced. New gaskets for it at least. Hopefullly your engine gaskets are ok, that's the first thing I thought of until I saw it was a 2 stroke.

Has it been laid up for months? Did you leave any gas in it untreated? You may need to boil out the gas tank . Try a carb cleaner first that you add to the gas.Check the plugs.Are they black/oily (too rich / worn ring), Tan ( correct ).they tell a lot about the condition of the engine. Good Luck