In short, they said "de-register it" (but I think un-enabling the credit card could also work). Here's Amazon's reply:
Hello from Amazon.com.
Thank you for writing to us about restricting a registered Kindle from purchasing content from the Kindle store. One way to do this is to deregister the Kindle from your account. When you want to add content to that Kindle, you can simply re-register the Kindle to your account, make a purchase or download content that is already purchased using Content Manager, and then deregister the Kindle.
To register or deregister Kindle on Amazon.com:
1. Visit
http://www.amazon.com/manageyourkindle
2. Sign into your Amazon.com account
3. If Kindle is not registered, complete the registration instructions provided.
4. If Kindle is already registered, adjust the settings in the "Your Kindle(s)" section.
You can also change Kindle's registration directly from the Kindle menu. I've included instructions for that below.
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HOW DO I CHANGE REGISTRATION SETTINGS FROM THE KINDLE MENU?
If you have access to the Kindle and prefer to change registration directly, follow these steps:
1. Move the wireless switch on the back of your Kindle to the "ON" position.
2. Press the Home key to make sure you are on the Home screen.
3. Scroll to Menu and press the select wheel.
4. Select "Settings" from the menu.
5. Scroll to the Account Name section and select "Deregister."
6. Select "OK" from the confirmation screen or select "Cancel" if you wish to abort the process.
7. Wait for Kindle to process the request. The account name will be blank and the Register option will appear when deregistration is successful.