Hello @Jane500,
You say that you don't have gas but is there any other form of heating within the house, including a stove, open fire, oil boiler? Any of those can also give off carbon monoxide?
Even if you don't have any of those it looks like Airbnb's terms for business travel simply require a detector to be installed. There are no conditions mentioned in the terms. What makes a listing business travel ready?
They do also say that they may make detectors available free to some hosts. There's a red "Get one for free" button at the following link but conditions apply.
https://www.airbnb.co.uk/home-safety
If you can't get one from Airbnb, battery ones are available from hardware shops from about £25.
Steve.