Capability to be able to purchase private product

I’m not sure about this approach to use a Private product. I would create a user role like you said and then using a hook hide that product from all others. There may be an app out there. I think it’s called Shop by User Role for WooCommerce or something.

However, this will require the user to be logged in to see it too.

This might do what you need.

Thanks. I think that’s what I’ll do.

I have a custom role because we want some users to have a custom dashboard (only access to certain things).

If you’ve built a custom dash for certain roles, you’ll have to write a hook for that too. However, talk to YITH. They have some great products.