@Ronald482 I charge a flat fee of $75.00 for up to 2 pets per stay, regardless of the number of nights the reservation is for. This pays for the extra cleaning charged by housekeeping, and is less than a guest would pay to a kennel. However, when the pet fee is charged at booking, AirBnB divides it by the number of nights, so if my guest changes their reservation from a week to 2 nights and I accept the change, they are going to be paying less ($75.00/7 times 2) for their pet.
For pet friendly hosts who wish to charge a per night fee, I guess that you would have to up your nightly rate or do as @Sarah977 suggests and document in your listing that the pet fee will be charged through the resolution center at X dollars per night, and NOT enter a pet fee on your rates page.
AirBnB has supposedly smart programmers -- there should be no issue with providing hosts with suitable programming -- either a nightly fee, per pet, per stay, OR a one time charge.