If it runs it is not the coil. Most common problem I have found with this style engine is the voltage regulator is bad. The charging system varies depending upon the model, type and code stamped into the valve cover. These are the two current styles of voltage regulator.
If the system uses one of these, it should be on the side of the engine. Find it and check the connections and wires. If all looks ok, disconnect the red wire and check voltage at tractor side with engine off. May have to have key on. Voltage should be same as battery voltage. If not there is a problem from there to the battery connection. If voltage is good then it is either the regulator or alternator. To check alternator unplug yellow wire from regulator. With an AC volt meter test voltage at yellow wire with engine running at full throttle. Each wire should be at least 14 V AC. If it is then you have a bad regulator. If low or no voltage, either the alternator is bad or the charging magnets on the inside of the flywheel have come loose.
If it has no regulator and all wiring is good it most likely the alternator or magnets. Check for battery voltage at the engine connector. Should be a red wire. This is all figuring on the wiring has not been messed with of course.
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