using SSL for all exchanges
Should be done no matter what solution you use, as long as credit cards/payment info is involved. As you probably know.
encrypt the data in a number of cookies that are stored locally having
the cipher as a confirm password that must be entered each time.
forcing the cipher to be strong, say 15+ mixed chars, and this is
confirmed by checking a hash of it on the server.
I usually remember my credit card number, and I'd rather put that in (as I'm already intent on not disclosing it to anyone) than a long and complicated key that most customers would write down somewhere anyway.
Even if we aren't allowed to say "don't do it!" - why don't you ask us for good ways to dissuade your manager from taking this decision? ;-)
What makes you unwilling to store this server-side? It's not like Amazon stores my credit card info in a cookie. The basic idea is to store all user info on the server, and access it when a user has authenticated successfully (i.e. logged in).
Cookies are in this case used to persist the logged in-state between browser sessions. The info this logged in-session has access to is stored on the server. With credit card info this usually entails a lot more security than other sensitive info, but it's the same basic idea.
Storing actual credit card numbers in cookies (encrypted or not) could be a potential PR nightmare when some tech-savvy customer realises what you are doing.
Thread for more reading: What information is OK to store in cookies?
Edit: The more I read through this question the more dumbfounded I get. Does your manager even know what a cookie is? How it works? What the point of it is? Saying that you want to store credit card info in cookies is like saying you want to use shoes as a means to transport shoe-laces. He is actively and purposefully shooting himself in the foot for no reason whatsoever. What he wants to achieve can be achieve a lot easier with other, much safer techniques - without any loss in functionality whatsoever.
From an article linked by Scott Hanselman:
Storing Credit Cards
If you absolutely must store credit card data it should be stored in encrypted form.
There are various compliance standards (specifically CSIP and PCI) that vendors are supposed to follow that describe specific rules of how networks need to be secured and data stored. These rules are fairly complex and require very expensive certification. However, these standards are so strict and expensive to get verified for that it's nearly impossible for smaller businesses to comply. While smaller vendors are not likely to be pushed to comply, not complying essentially releases the credit card company of any liability should there be fraud or a security breach. In other words you are fully responsible for the full extent of the damage (realistically you are anyway – I'm only echoing back the rough concepts of these certifications).
(my emphasis)