I revisited AwoCoupon and this time around managed to get it to work. There seems to be a bit of a quirk, at least on my installation. If you make only one coupon, then that discount will be applied to the specific product regardless of whether a coupon code is entered or not. In fact the code field does not appear on the checkout page in VirtueMart though the discount is applied. If, however, you make a second coupon, even an unpublished one, the field appears in the checkout procedure and works only for the specified product as intended. That solves my problem once and for all.
Ideally, of course, VM will implement some additional parameters for coupon deployment though they seem reluctant to take this on for whatever reason.