What engine is in the 104? I believe a few voltage checks will tell you what is happening. One side of the coil should have battery voltage with the switch on. The other side should show battery voltage with the points open and zero volts with the points closed. Start there and see what you have. If you can, slowly turn the engine over by hand to check the side of the coil connected to the points. That's also a good way to locate the points, just follow the negative lead from the coil to the points.
If you have the model number from the engine, you should be able to find points at any good auto parts store or cub cadet dealer, TSC etc.
To answer your question, yes, it could be the coil, but there are other more likely sources for the problem which are cheaper fixes as well.