By using Zapiet - Pickup + Delivery you can automatically apply a discount code to all of your delivery orders.

Requirements

You will need to have a discount code created in Shopify.
- To add the discount code, you can follow the Shopify YouTube tutorial in their Discounts guide.

Add the discount code in Zapiet - Pickup + Delivery

Open Zapiet - Pickup + Delivery and click Settings.
Click Local delivery.
Find the Discounts section and enter the discount code you created in Shopify.
This field is case sensitive—"Delivery" is not the same as "delivery".
You can only add one discount code at a time.
Click Save.

Your delivery discount code should be automatically applied at checkout.

Only one delivery discount code can be added at a time.
If a customer uses this discount code, then goes back to the cart and chooses a different checkout method, the discount code will still be applied.
To get around this, you can add a discount code in Shopify for a discount of 0.00, and add this discount code into your shipping and pickup settings.
As this is a Shopify discount, customers can copy one checkout methods discount code and apply it to another. There is no way to stop the discount code from working if a customer manually adds it in—this is a Shopify limitation.

Check that the delivery code added in Shopify is the exact same as the one added in Zapiet - Pickup + Delivery.
Check that the discount made in Shopify is a discount code (not automatic discount).
Check if you're using an incompatible app.
If you are using multiple discounts, check which discounts can be combined.