You can add discount codes that will show up in your Back in Stock emails if the particular variant that was requested has a discount assiociated with it.
You can add discount codes as you usually do in the Shopify Admin UI. Click on 'Discounts' on the left and add some discounts associated with your products. You can add association by collection product, variant.
Once you have added your discounts, it is time to import them into Back in Stock.
Open up the Back In Stock interface, and click on Settings. From there, find the tab that says 'Discount Codes' and click it.
You should see an option to Enable discount codes, which should take you through the process of authorizing an additional permission on Shopify. After this, you should now see the option to Import Codes and Sync Codes.
Clicking on 'Import Codes' will allow you to choose particular Import Codes from Shopify and add them to your list. If you change these codes after adding them, you can Sync them with Back in Stock by clicking on 'Sync Codes'. Otherwise they will be synced nightly.
To add Discount Codes to your emails, first go into your Campaign by clicking 'Campaigns' in the left side navigation.
Now, click on an action that sends a notification. Notice you can edit the template below, so click on 'Edit' for the Email template.
You should now see a new section in the Email Templates that allows you to add in discount codes.