Can I discount the sale price to create a down payment?

No.  Lenders provide financing based on the sale price or the appraised value, whatever is less.  In the case of a "discounted" price, say selling a home worth $250,000 for $240,000, the sale price is $240,000.  Lenders do not recognize a discount. 

A better approach is to pay full market value but to make the transaction dependent on a "seller contribution" at closing.  The effect is the same, but the accounting makes more sense to lenders.

Thanks,

Aaron