When admins want to give an affiliate a discount on their membership dues, admin should create a custom billing.

Menu Path: Affiliates module -> Affiliates

Find the affiliate and make sure they have the correct affiliate category on the Affiliate Profile tab.  

On the Orders tab, make sure an order exists for the correct membership category. If one does not exist, create one now.  Select the checkbox next to the order, then click the Create Billing button.  Select Custom Billing.

A pop-up will open that will allow you to change the start and end dates for the membership period, as well as the amount of the invoice.  The amount of the invoice can be edited with or without a discount.  For recording purposes, you can select the Add Discount button which will allow you to enter the discount and a discount reason.

When you are finished entering details, click the Create Billing button and the custom invoice will appear on the Affiliate's Billing tab.