How can I add a website to Notification Center after denying its initial request? For example, when visiting eBay.com or cnn.com, a dialogue box pops up asking if the site can send notifications to Notification Center.  

If you initially choose deny, but change your mind later, how can you go about adding a site back to notifications (manually or otherwise)?
You can select the site and revert the changes on Safari → Preferences → Notifications.