Your tractor was originally equipped with a Kohler K-321 AQS engine. Those use a points, condenser and coil ignition system. The stator coil is there for one reason and that is to provide power to recharge the battery and run the rest of the tractor.
If you have no spark, then you need to diagnose why in a logical fashion.
You need a multimeter to make your life simpler.
Set the meter to the DC volts scale. Open the hood, turn the ignition key to ON. Put the black probe to the negative post of the battery and the red probe to the coil terminal that is marked +. You should read 12 volts. If you do not, then perhaps a blown fuse or worn out ignition switch is at fault.
Turn the key to OFF. Remove the wire from the coil terminal marked (-) . Take a jumper lead and connect one end to the negative post of the battery. Remove the spark plug and put the plug wire back onto it. Lay the plug against bare metal of the engine head and place something heavy on it to hold it down tightly. Turn the key to ON. While watching the gap of the spark plug, touch and remove the other end of the jumper wire to the (-) terminal of the coil several times.
If you get a spark, then the coil would appear to be OK and also the spark plug. The problem is most likely the points. Remove them from the engine. Use one of your wife's emery boards that she has for manicuring her nails. Insert that emery board between the points and file both points completely flat.
Make sure that you do not get any oil on the points. Install them and set the gap to 21 thou. Try starting the engine once you install the spark plug after re-gapping it.