Paypal used to not work properly with negative values, so we apply the discount across the product price to come to the correct result.
I think the paypal documentation says you need to use one of their advanced checkout solutions in order to support discounting, but in reality I think you could probably add it as a negative line item. You would have to check but I believe the newest version of the paypal standard service started supporting negative line items.
The updates would be done to the hidden form elements on the confirm page. You would have to adjust the current price field so that the adjustments aren't made automatically and then add the discount as a final line item. It may not work but that is a possibility if the price adjustment solution doesn't work for you.