I would like to set up a private coupon code for my business cards, that only the customers that have the code can use. How can I do that?
You just make a regular coupon code.
@CrochetMarga: You want to "Create a promo code" on the Sales And Discounts Page https://www.etsy.com/your/shops/me/sales-discounts
Just be aware that there is no such thing as a private code.
Once you send out that code, it can be shared online or scraped by coupon sharing sites.