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For unreasonable discounts, I’ve declined curtly with, “I’m sorry that I cannot accommodate your request.”
For someone who seems a bit more reasonable, I would explain the built-in weekly/monthly discounts and if they are still interested, they are welcome to book.
Back again…
Message from “J”: I noticed your listing originally said $58 for tonight. can you honor that? Also, may I do an late check out (2-hours past your check out time)?
Me: I’m a little confused by your questions, because the price you mentioned is what is on the listing now…? Are you are asking me to pay or waive the fees or taxes?
“J”: It says 58, then when I enter the page it says 65 then when I go to book it says 73. I understand there are fees and I’m not asking you to pay them. I was just hoping the base cost would be 58 instead of the 65.
(She must think I’m stupid. I search for my place to see what she is seeing on the website…)
Me: Correct. After the $58 for the room, there is an additional amount for the Airbnb Service Fee $7, and also City Occupancy taxes and fees $8.
(It’s right there in black and white! Duh!)
“J”: Ok. Are you able to discount that price at all for this evening? Also are you flexible on check out time?
Me: Sure! I’d be happy to host you with a 25% discount for 1-night and have you stay past the check out time at no additional charge. Gladly! Is there anything else you need? I could fill up your car with gas and take it to the local car wash too. Breakfast in the morning? Absolutely! What’s mine is yours.
Ha, ha… what I really said was: Good luck with your search. There are other rooms on Airbnb that are in your price range. (Airbnb site indicates that the average price in the area is $80).
My approach is a little different when it comes to discounts. First, about 90% of my guests don’t ask for discounts. I do get requests from military and teachers for discounts; for those, 10-15% is normally provided. For repeat guests, particularly for those who left great reviews, I’ll often provide them with at least their original rate (we go up about 10% a year) when they booked. Finally, when a guest wants to extend their stay, we’ll often do it at a lower rate (I love extra nights - doesn’t increase my time for cleaning), and we have significant discounts for week or longer stays. We run a very flexible operation, from cancellation fees to scheduling, and we get great reviews as a result.
How about retired teachers? 
I consider myself flexible in many ways but I don’t give discounts to people who ask, but I’m rarely asked. But I’m also just a room at $50 a night or less, no cleaning fee and lots of one night stays so not much wiggle room. But higher rates and longer stays, say $200 a night, I’d probably have more flexible pricing. I also get great reviews but can’t point to one thing.
Hi, Katnhat. Sorry, I haven’t been on this forum in a long time. Yes, after about 3 weeks, she sent the sweaters, and they were nice. However, she contacted me asking for the same rate over Christmas – which always gets booked. I turned her down, which I’m glad I did, because I got guests for 5 nights for $250/night. She wanted 2 nights at $100/night over the weekend. When I told her that her request was for a busy time and that I could not honor that price, I never heard back from her.
Would I do it again? No. It wasn’t really worth the hassle.
I very rarely get enquiries for discounts, but they can be accompanied by daft requests. My response is “good luck and God bless”!
Thank you so much for considering my home. I feel I offer excellent value for the quality property and the amenities I offer. I am sure if you keep looking you will find something that fits your budget.
You don’t know how many times Ive wanted to send this type of message 
It is my experience that the cheapest guests are the worst. They will have the least respect for your home and house rules and have an entitled attitude. You just can’t satisfy them even if they were staying for free. Just say no and no need for any explanation… if they get mad at you for this, you should be happy because that means you made the right choice.