Ok, it's called non-owner insurance, and it's usually reserved for people who drive w/out compulsory insurance and have a history of accidents, so the courts force them to take out some form of liability ins.

Here's what I did. We sold our car before moving to Oz, but we still had a bit more time in the US to go visit friends and family (3-4 weeks) during which we rented cars. So, right before cancelling my insurance, I contacted AIG (our insurer) to get a non-owner policy. They wrote me one out of a subsidiary agency. You might want to check with AIG, or with your last US insurer. The magic words are: non-owner's insurance. They should be able to help you once you mention that. You might have to send in additional info, including driver's records and such. In my case, they required a minimum 6-month contract, but I was allowed to cancel when I no longer needed the service, and I got a prorated refund (minus a small cancellation fee). For anything longer than 2-3 weeks, it might be worth the trouble.

I don't know if any insurance agency will offer such a policy to non-US residents, but if you can claim to be dual resident (I could at the time; a bit more iffy now), it should be no prob. The fees are a bit higher than you would expect for similar liability coverage, and that's because the majority of people who are forced to take this insurance are so accident-prone. Nonetheless, it beats having to pay the outrageous fees that car hire agencies offer. Good luck on your upcoming trip!