The coil is under the flywheel ... but it starts back up ... I would not think you have a coil problem...
First check if it is a fuel problem... spray any flammable liquid into the carb... even WD40 will work as a temp fuel..
all you need to make an engine run is fuel, air, compression and spark all at the right time...
I think you are having a fuel problem. Establish that with another fuel , and then it will be easier to track the problem.. .:smile:KennyV