Apple - How to disable notifications for a single mailbox in Mail?

To disable notification for certain Mailboxes you can create Smart Mailboxes for the accounts that you want notifications, and change the settings to enable only them.

1. Create a Smart Mailbox through the menu Mailbox > New Smart Mailbox including only the Accounts that you want to receive notifications.

   

2. Inside Preferences > General change the Dock unread count and New message notifications putting the name of the Smart Mailbox or group of Smart Mailbox created.

   

The simplest way I can think of is to remove the general New Message sound...

Then add it back for specific accounts...

This is a simplified version of the method I use for rules splitting emails off to different folders per purpose. I only want to be notified for the ones I consider important, not every Facebook announcement.

Edit:
I just realised you might mean the actual banner notifications - this, unfortunately can only be honed in very broad strokes...

I've found the solution to that is if I don't want to be notified, I use rules to move to another folder, one which gets no notification, i.e. not Inbox.

This does mean you can end up with quite an array of folders... but each serves a purpose.
I actually normally leave the sub-folders closed, including Inbox, because the account they came to is no longer an important part of the filing.