A zipped archive is only helpful if it is encrypted with a password, and the password is not sent via email. As well, the customer would need to ensure they're following the instructions exactly to get it working. Does their OS support the latest encryption algorithms that an external program (i.e Winzip or 7zip) support? If not, you'd also need to walk them through installing the extra programs.
In reality, I see two ways to go about this if you're adament about obtaining their credit card information: through a payment processor, and not-at-all.
Payment Processor (i.e. Moneris, Global Payments, Paypal, etc) take on the security burden, and deal with the encryption required. They will take a small percent off the top, but you will have money, and the customer has security. Win-win!
If you are purchasing services on behalf of a client, I would suggest getting payment up front (and obviously with a bit of markup - what happens if they don't pay you or forget for a month?), and then purchasing the services. If you're doing web hosting, there are many top-tier solutions to manage this part for you (i.e. cPanel).
After the services are running and the client has paid, I would send them instructions on how to add their CC information to the payment portals, removing you from the accounting side of their account.
A BIG WARNING HERE: You mention you only deal with the customers over email? How do you know they're really who they say they are? You are taking a big risk by offering to handle everything for this client without meeting them in person. I would suggest taking a few precautions, such as only getting services for as long as you can afford (for if/when they don't pay), or even using a temporary credit card number (Visa offers this service, not sure about others) that has a preset limit on how much can be spent, even though it goes to your main credit card.
You also do not want to become involved in any sort of scam with stolen credit cards. The less you deal with their credit card on your end, the better. If you can avoid taking the credit card number during the transactions, the better you'll be!