I believe my coil is bad on my Onan 4BGE generator

I don’t know the difference in the two coils you show but you did clean the corrosion out of the female sockets on the coil ? That gen will run on one cylinder so I would check the other plug wire too. SR Sales has a lot of old onan parts call them. https://www.srsoemparts.com
You’ll have to call them tomorrow. Go here and post your problem too.
https://www.smokstak.com/forum/forumdisplay.php?f=1