I'm struggling with this issue as well - and would like to see a per-line-item Discount feature be added.  I'm adding Invoices via the QBO API, though.  The documentation for the API SEEMS to imply that it IS possible - but it doesn't work. 

The documentation describes these attributes:

SalesLineItemDetail.DiscountAmt

SalesLineItemDetail.DiscountRate

So... if you can't add a per-line discount directly to an Item line... what is the point of the API attributes?

The presence of these attributes in the Create Invoice object certainly implies that it is possible.  But every time I add those attributes to my object, they appear to be ignored.  Which matches the user experience for QBOnline that is being discussed here.