First and foremost, figure out how to make the payment. If I remember correctly, the payment needs to be 30 days delinquent before appearing on your report. At this point, if you've made no payment for two months your report probably indicates a 30 day delinquency and will probably ding your score a little bit. To my knowledge there's no way around that, so there's really no reason to lose any sleep over it. You missed the payments you'll have an extremely minor blemish on your credit history. Online payments are a convenience, find out the address and put a check in the mail.
Once the bank has processed your check, call the customer service people and very calmly and pleasantly explain the situation to them then ask "is it possible if you could please can you reverse these charges."
In my life I've had several situations where some charge would hit a sock drawer card and I'd miss the payment. I've always just paid whatever interest resulted but I would call and ask very nicely, "is there any way you could please reverse this charge," they'd reverse the late payment fee.
Always be nice. Don't bore them to death with your life story. Don't make this the bank's fault. Just ask nicely if they can reverse the late fees.
It's worth mentioning that though I've missed several payments over the years zero of those have appeared on my credit report.