In the desktop editions you can calculate per-item discounts with the FormCalc SST for QuickBooks add-on, or possibly also with the CCRQInvoice add-on (I'm less familiar with it). 

In general this would involve adding a couple custom columns to your invoices (or sales receipts or...whereever you want to calculate discounts). Then in day-to-day usage you would enter a discount amount on each line, and the add-on would calculate a new Rate (price) on each line. With FormCalc SST you could see what the discounted Amount is before saving the invoice. (CCRQInvoice is more of a batch product--does the same things but not in real time.)

In either case, you could also set aside a customer custom field in the invoice header to use as a default discount rate for each customer...so the add-on would use the default discount on Item lines where you hadn't entered a different/specific discount.