We used to offer multi-night discounts, but getting people to stay two consecutive nights in our area is extremely difficult, and we would get guests spending their first night in town and then their last night in town before heading back home and would ask for the multi-night discount. We are located in a city no one wants to visit, but have to if they take a flight or a cruise.
We have since started to partner with local outfitters (fishing, flight seeing, photography tours, etc) and built multiple night packages (lodging and day out with the tour operators as the main selling points). Most tour operators offer a 20% discount and with many tours exceeding $3,000 for a group of 4, the discount we pass onto our guest far exceeds two nights. It has not been uncommon for the guests to still only stay one night, but we have effectively reserved the room for two nights. In my younger days I may have opened a room up, but now I just keep it blocked off and enjoy the little break.
We had to think what type of operation are we and does that warrant guests wanting to spend more than one night with us. Personally, I don't think any reasonable discount will sell a second night. Make them want to spend the extra night(s) with you or look at ways you can advertise local businesses and outings that makes multiple night stays make more sense to the guest.