Hi there, it sounds like you are having the same problem with your Haterette as I had earlier this year. I would recommend you check the points and capacitor. I can’t remember just how much the parts are but they were really cheap. The B&S replacements had pretty good fitting instructions enclosed along with a small tool to enable removal and reconnection of the wires.
You mentioned replacing the coil, the gap should be set to 0.25mm-0.36mm using a non-ferrous feeler gauge, using a ferrous one could weaken the magnets (so I have been told) I used a thin piece of card which worked just fine.
Before going to the spares shop, I’d suggest you check the flywheel key. I had an engine once which had distorted the key and upset the timing.
May I also suggest you check “Youtube” there are a few interesting videos on there showing various repairs/fixes for similar engines.
Good luck, Ray
Ray, October 2010