The picture you have is of an OEM coil for later airhead bikes .
You need to due some troubleshooting, before replacing parts .
How old is the battery ?
Is it a serviceable type, or sealed ?
If it's a serviceable type, what is the specific gravity of the electrolyte when it is fully charged, should be 1.290 fully charged .
If the battery is suspect, wouldn't be a bad idea to have it load tested to be sure it's at fault, just to be sure .