How can a foreign pilot get renter's insurance in the USA?
Most flight schools in the US have an easy policy for renting out their planes:

You go there, you do a checkout flight on an airplane with one of their instructors, and you can go ahead and fly as much as you want.

The planes are then insured by the flight school, and you pay for the insurance by paying an hourly fee to the flight school. The checkout flight is necessary for the insurance, and is most of the time valid for 90 days. After that, another checkout flight might be required. 

You, though, might not be included in that insurance. If something happens to you, the flight school's insurance will probably not cover the costs you might have.

I don't want to advertise on here, but for if you are interested I can show you a nice flight school in Florida.