This might help also it is a older post from Jeremiah C.
A capacitor is not expensive, and they should be replaced every couple of years anyway (although Dennis may tell you he's still using one his father installed in 1940). The coil is fairly expensive and there are several tests available for it.
1. Do you have 12 volts at the positive terminal of the coil when the key is on? (Measure from frame to terminal.)
If so, the safeties are working and the primary circuit wiring and ignition switch are OK.
2. When the points are open, you should also see significant voltage from the negative terminal of the coil to ground; but almost zero volts when the points are closed. If you're seeing significant voltage swings as the points open and close, then the primary winding in the coil is OK. If the voltage never changes as the points open and close, something is very wrong. (It sounds to me that this is likely your situation.)
From Kohler Service Manual TP-2379 for Kohler single cylinder engines
Note: The capacitor charges each time the points open, its purpose is to keep the current across the points to a minimum, thus preserving the points. You should NOT see much spark at the points, just a little when they open, as the juice is supposed to be diverted to the "condenser." When the points close, the capacitor is discharged.
To investigate further, turn off the key, disconnect the battery and get a Digital Multimeter that can read capacitance, or grab an analog meter with an Ohm scale, preferably witb a 1 kilohm range.
3. Disconnect both terminals at the coil (+) and (-) as well as the spark plug wire and measure the ohms across the primary winding, from the (+) to the (-), it should be very low, just a few ohms, since you're simply reading the resistance of a length of wire; then I believe if you measure from the negative terminal to the terminal for the spark plug you should get a slightly lower reading, since I think the coils are fewer and the wire is thicker. If your meter shows either open or a dead short for either of these tests, the coil is burned up. (You might also try reading from the case to each of the terminals to see if one of the windings has shorted to ground.
Note: I think there is a resistor wired in series with the primary winding inside the coil, so the primary will definitely read higher than the secondary winding at the spark plug terminal.
4. If the coil checks out, and I hope it does, you can test the capacitor thus:
For an analog meter, touch the terminal to the case or other ground to discharge the capacitor and then hook up the leads with the meter set to a fairly high range for ohms, you should see the needle jump up and then "subside" back to zero as the capacitor charges through the meter. If the needle fails to move significantly, or you think you missed it, discharge the capacitor, and try it again using a different range on the meter, I think higher is better than lower, but my memory could be failing me.
On a Digital Multimeter, set the meter to read capacitance, discharge the condenser, and take a measurement.
5. If the primary ignition circuit checks out, then the problem must be in the secondary. Swap out the spark plug wire, and/or try a new spark plug.
I believe a bad condenser will typically show itself as weak spark before failing completely.