Renting a teardrop trailer:
If you are renting a teardrop trailer for a test drive or weekend getaway, the liability coverage is tied to your tow vehicle and your existing policy. You should have liability coverage on your tow vehicle by law. Some rental companies will require that you show your proof of insurance and you can request that from your insurance agent. This proof of insurance is called a binder and can be printed or emailed to the rental company. The amount of coverage will depend on your type of insurance account.
Supplemental insurance might also be a good idea. This type of insurance might be offered by the rental company and it will provide additional coverage for bodily injuries or property damage if these are not covered under your current insurance. At the same time, you can also purchase Personal Effect and Personal Accident Insurance for your own personal possessions, e.g. just in case something is stolen from the rental trailer.
Renting out your own teardrop trailer:
Renting out your own teardrop trailer is a different story. Most insurance companies will not cover your trailer if you decide to rent it out to someone with an unknown (to you) driving history. For this case, you will need to contact a local insurance broker to purchase insurance specifically for renting out your trailer.
These types of brokers are familiar with businesses who regularly rent out campers, trailers, moving vans and other mobile units. The type of insurance they will recommend and sell you will have a different kind of liability coverage and will consider more moral logistics like the safety qualifications of your own trailer and the driving history of your customers.
I spoke to a representative at my own insurance company, Geico, and they said that if this type of insurance is purchased for a trailer—they will remove the trailer from the current vehicle insurance since they do not insure for rental businesses. Keep this in mind if you decide to rent out your personal teardrop trailer.