Can Airbnb book for 2 months, and can I negotiate the price for my listing with a guest?

[Clare0]

@Jeanne13 The short answer is Yes and Yes.  But seeing as how you are a new host I would advise against it.  Unless you have a background in real estate rentals in California you may not be aware of problems that may arise out of long term rentals.   You should read this Airbnb article about Long Term Stays: 

https://www.airbnb.com/help/article/805/what-are-some-things-i-should-consider-before-hosting-long-t...

I've set my maximum night stay to 21 just to avoid the tenancy rights that renters can assert for stays longer than 30 days. 

But, if you decide to proceed, you can respond to an inquiry, not a reservation request, with a Special Offer. 

https://www.airbnb.com/help/article/35/how-do-i-send-a-guest-a-special-offer

Good luck!