Discounts are added to purchases and subscription products on a customer, rather than to the customer itself. The following are steps to add a custom discount to that customer's subscription products.
To add a discount to a subscription product:
- Navigate to the customer's active subscription product.

- Select the Discount option for the Advanced Overrides field on the subscription product and click Go.

- A pop-up will appear, click Add Discount.

- Enter the values for the fields, click Add and click Apply.
Note: Periods are the same as the frequency of the subscription. E.g. If it is a monthly subscription, then the period is in months.

Save the changes for the subscription product.

Information on how to add discounts to multiple customers at a time can be found here Creating and Applying Discounts and Coupons Overview