The only way to offer a discount to clients booking online is by creating a Service Promotion or Gift Certificate Promotion, which automatically offer discounts to any clients using the Promotion link to make their purchase. Currently, there is no way to create a Promo Code or Discount Code that can be entered by clients during checkout to automatically discount an online payment.
If you wish to create a Service Promotion, you can do so by following the steps here: Creating a Promotion for a Service.
If you wish to create a Gift Certificate Promotion, you can do so by following the steps here: Creating a Promotion for a Gift Certificate.
If the discount is only meant to be available to a select group of clients, you can create the Promotion as "Private" and the discount will only be available with the clients that you share the Promotion link with. Once the Promotion has been created, you will then need to copy the link to the Promotion and share that link with the clients that you wish to receive the discount.
You can also Create a QR Code for the Promotion page to distribute the discount on physical media (business cards, flyers, etc.)