@Lisa658 - there is no way to provide a "free" stay, as you just enumerated. At best, it's a "discounted" stay. Advertising one vs. the other can cause legal ramifications. You can, as I advised, write off an entire gift card purchased to support a cause.
Also, as the host, you have no contol then who purchases this "gift". You have to say yes whether they are verified, a felon, maybe even someone who couldn't qualify under Airbnb policies as is. You have to say yes to this guest whether you are comfortable with them or not.
Let's just think about some "what if" situations: What happens if the guest damages your property while they are enjoying this free stay? Assuming that you've collected a security deposit as normal, now this situation gets sticky. It's not a business transaction, it's a charitable one. What if they break your house rules or have a party and you have to have the guests removed? We all know how difficult this is with paying guests, let alone ones who think their stay is "free". What if you as the host have a problem and have to cancel? They cannot rebook another location with your "gift". A charitable gift is a legally binding contract so if you cannot fulfill the contract - let's say your property gets torn apart by a tornado - how will you fulfill the contract? Unless you put restrictions on the gift, those getting the donation could potentially use it during the most valuable weekend you have on your books. You can't say no without saying so in advance. I'm sure there are so many more "what if" situations....these are just the few. And before you say it - everything could go smooth as silk, no tragedies or drama, that the risk is worth the value of the donation... true enough.
Finally, Airbnb washes their hands of any liability that comes with donations:
Donations
Some Hosts may pledge to donate a portion of the funds they receive from confirmed Bookings made via the Site, Application and Services to aparticular cause or charity. We do not take any responsibility or liability for whether the Host does in fact make the donation he or she pledged to make. In such cases, the Host in question is responsible for his or her own compliance with all laws and regulations applicable to such pledges and/or fund-raising.
(My fear here would be if they wash their hands of the liability of actually giving the gift, they will was their hands at supporting the gift itself, not a road I want to go down personally.)
The point for me being is that the risks outweigh the value of a little bit of "advertising". If you are doing it out of the goodness of your charitable heart, go forth and give away! This is what is great about the free homing services Airbnb provides for people when there are displaced persons - you can donate your space to take people in. The amount of additional traffic to your site to get a few more bites on stays does not, to me, outweigh the risks. If you are supporting a charity that makes you proud to do so, I can't, for the life of me, come up with a reason to not take the risks outside of the ones I've already provided.
However, for me, I'd buy a gift card and let the guests stay where and when they wanted and write the entire purchase off on my taxes. The organization can still promote me as the donating host and my listing as the contributing offer, but it relieves me of most of the risks associated with a physical donation of space and gives more freedom to the people getting the charity. Heck, they may not like me - that reason alone would keep me from wanting to force them to stay in my property!
JM2C