There's 5 ways to discount price that I can think of...
1. Set your minimum nightly price lower in pricing settings. Somtimes Airbnb prompts you to do this in the calendar as a tip, typically with a suggested amount to lower to be competitive with other area listings. I do not know if this increases visibility on search results, but I would guess that following Airbnb's suggestions does put you in a favorable position in their algorithms.
2. Set your weekend price higher than your week night price in pricing settings. However I believe you have to turn off Smart Pricing to do this. I do not think this shows in search and I think turning off Smart Pricing hurts your listing more than helps.
3. Manually change a price for certain dates. In the calendar if you highlight dates you'll see an option to manual change the price for just those selected. You can do this with Smart Pricing on, you'll see the prices for those dates turn grey since they are no longer under Smart Pricing. I do this for when I know there is an event nearby and surge pricing or if I really want to fill those dates. This does not give your listing any extra visibility though or notify Airbnb that you've accepted a 'tip'.
4. Send a Special Offer for a requested booking. This you can do within the message of a certain guest/booking request. This only applies for that reservation and is not visible to anyone else but you and that guest. It's a way to encourage that induvidual to confirm a booking or to make special allowances that you might have discussed with them.
5. Set an Discount Offer for selected dates. This is the best option and the one I believe everyone is referencing here. I do not believe you can do this unless prompted by Airbnb. Or at least, I haven't found the way to do it on my own. It makes sense though because, if you apply a discount, they put your listing in an email marketing blast to users who have been looking in your area for those dates in the hopes that it gives you lots of extra visibility and book incentive. I've had a good amount of success with it when I accept the 'tip' exactly as prompted by Airbnb. You have the option to change the percentage (though not dates, if I remember correctly) before you submit if you like. Since it would be easy to 'game' this system by setting your price high and then always giving a discount to get the visibility, it makes sense that it is only available when prompted by Airbnb. If anyone knows how the Airbnb algorithm for this works, please let me know.