Your CB200 runs entirely off the battery, so the alternator is irrelevant in this problem.
The battery, in fact, is the FIRST thing you check on any of these old Hondas - if it doesn't have enough punch to use the electric start, you're chasing your tail until you get a good strong battery.
If you have 12 volts at the black/white wire to the coils (umplug the coils for a minute), with the key on and kill switch at "Run", then it's either coils, condensors, or points.
I replaced my CB200 coil with half of a SOHC 4 setup = one coil with two plug wires.
Off EBay, it cost about $25, was a stone cold bolt-up. With new plug caps, it gave me a BIG spark.