@Kathie89
Offering a discount is up to you, but as you pointed out, it's difficult to determine if it is legit. Many Hosts don't offer these for that reason.
Also, I have found most guests looking for a "discount" generally turn out to be problematic. Many Hosts have a polite Quick Reply created that says while they appreciate their service the listing is already competively priced for the amenities, location and season and unfortunately you won't be able to discount further. If you have a weekly or monthly discount that applies you could mention that. Then conclude with you hope they able to find other accomodations that would better suit their budget.