Ouch at the price of the coil, I usually sell them second hand for $20 or so.....
Anyhow To change the coil is simple enough, you need to remove the engine from the mower frame, flip it upside down and swap the coils over. The coil-flywheel magnet distance is the thickness of a business card. Replacing the module is as easy as drilling out the rivet holding it on underneath the carby, and reattaching the new one.
It is also adviaable to replace the rubber boot and sock where the two wires go into the back of the carb as they can be a big cause of no spark issues.