Just to clarify a bit here:
View/Add to Cart buttons allow a place to enter a Discount Code in the cart before the buyer chooses to proceed to checkout.
Buy Now buttons bypass our cart and take a buyer directly to Checkout. Thus, any cart-based settings like Cart Shipping, Cart Tax, or Cart Discounts will not work with Buy Now buttons. However, as Stefanie said, you can use product-based Item Discounts with Buy Now buttons. These are configured as a "coupon code" for a flat amount off the unit price in the product's own settings.
Since Buy Now buttons bypass the cart where the code would normally be entered before checkout, you'd need to use a special version of our Buy Now buttons to let the buyer enter their code on your page before they click Buy Now. We have made this modification easy with a checkbox on your Buy Now button code screen: "Modify buttons to let buyers enter discount codes". That will give you button code to paste on your page that includes a text box for buyers to enter an Item Discount code you had configured in that product's E-junkie settings (this is what seacoaster was referring to above).
You can also make a Buy Now button that has a built-in Item Discount code, so buyers who click that special button (perhaps on a secret page you send selected buyers to) would automatically get the discount. You would take your regular Buy Now button code and add &on0=Promotion&os0=CODE (where CODE would of course be your Item Discount code) to the end of its button URL like so:
(That should be one long unbroken line with no spaces, but you get the idea.)