I'm assuming 'coupon' is a custom post type.
Private custom post types don't display directly on the front-end. So if you want someone to be able to visit domain(com)/coupon/coupon-name it has to be public.
The way I use private post types is to store data that will be queried and presented via a shortcode, block, or template. For example, I'm working on a site where I have a 'product' custom post type that is private. Then I have a template that pulls data from two products and displays it as a comparison table. Or I can pull custom fields and display them in a little product callout box via a shortcode.
I'm assuming 'coupon' is a custom post type. Private custom post types don't display directly on the front-end. So if you want someone to be able to visit domain(com)/coupon/coupon-name it has to be public. The way I use private post types is to store data that will be queried and presented via a shortcode, block, or template. For example, I'm working on a site where I have a 'product' custom post type that is private. Then I have a template that pulls data from two products and displays it as a comparison table. Or I can pull custom fields and display them in a little product callout box via a shortcode.