If you have a volt ohm meter you can check your coils pretty easily. You want to check the primary side and then the secondary side of the coils. On my kz550 the primary reads about 3 ohms the secondary about 13k ohms.
If your bike uses resistor caps on the sparkplug leads you should also check these, most should read about 5k ohms. I had a couple of faulty caps on my bike, one had infinite resistance the other was very high. The spark was very weak on these leads. I went ahead and changed my wire and caps as preventive maintenance.
Most bikes have an advance mechanism that needs to be cleaned and lubed periodically. Basically, as the rpm increased off idle the timing curve is advanced. This may be why your bike is stumbling. It could also be fuel related, when was the last time you cleaned your carb and fuel system??