Thanks for your question. First, you will need to contact Airbnb to see what type of insurance they provide while you have guests in the home.
I certainly understand your concern, but you cannot get a renters policy for an Airbnb you are temporarily residing in. If you have a renters policy for your current address, your liability coverage will cover any damage you cause to the Airbnb (up to your liability limit).
For all their homeowners, Airbnb provides Host Protection coverage that protect the contents of the house from guest damages. You will also need to get regular home owners insurance in addition to what Airbnb covers.
If you're referring to renting out your home on services such as Airbnb, I would recommend looking at what are called Homeshare policies. A few companies that provide them (in addition to the companies you mentioned) are Slice, Progressive, and Allstate.