@Mary4822
I host long term guests and have weekly and monthly discounts built in to my pricing. The nightly rate also reflects this, i.e. I set a minimum I am happy with (bearing in mind this will be lower according to the long term discounts I've opted for), but the nightly rate is lower than it would be for short term stays. So, if I then get any requests for more discounts for long stays, I just point out that the room is already discounted.
The important thing is to check out your local competition (comparable listings, not all of them) and price according to what you feel the place is worth and what makes it worth it for you to host, NOT what the guest wants to pay. There will always be guests who think they should get somewhere super cheap.
I would not recommend Airbnb for year long stays. You will get paid monthly, but if the guest doesn't pay after the first month, Airbnb probably won't do anything about it. Plus, there is really no real deposit if the guest defaults or causes damages. Perhaps tell the guest to book a shorter stay, i.e. three months, with the option of extending to a full year if all goes well, but that a contract and deposit will be required.
Most importantly, what are the regulations regarding tenants rights in your area? What you don't want to end up with is a costly and time consuming eviction scenario.