Hi finbar. Let's start with the easy stuff. Your data indicates that your engine is a 92502, which means it is 9 cubic inches displacement (148 cc), is of the second design generation, has a vertical crankshaft and a Vacu-Jet carburetor, it has plain main bearings and no built-in reduction gear, and it has a radial-pull rewind starter. At this point we have already struck trouble, because your engine has a horizontal crankshaft, not a vertical one. It looks to me as if someone has fitted the wrong cooling-air cowl to that engine, and perhaps has made other changes as well. I doubt there is any point in going into the rest of the information that can be gleaned from the model, type and code, since it seems unlikely they apply to your actual engine. However at least we now know why your Briggs & Stratton 3 hp decal is upside down: it is the correct way around for mounting on a vertical crankshaft engine.
Getting back to your ignition problem, did you try replacing the capacitor (condenser)? That seems the most likely cause of your problem. At this point I have no idea why you replaced the points.
If you try, or have tried, replacing the capacitor and this does not help, it would be time to consider whether to try replacing the coil, or alternatively, fitting a Magnetron ignition unit.
I suggest that you do not buy a Magnetron from a merchant without first asking our members to send you PMs with prices for second-hand units. You could do that through our Wanted forum.
