No. Donations are only deductible if they are made to a "qualified charitable organization". An individual such as a client or customer, is not, and can not be, a qualified charitable organization.
You should only be charging the discounted price from the get go, and that's it. But if you make a mistake (and people do this all the time) and charged the full price, then your return to the client of the difference between the full price and the sale price is dealt with in the "returns and allowances" section. That's the way to properly and correctly report a refund of previously recorded income.