Based on excellent feedback here on the forum we recently started using Bayside Rentals to rent out our place.
http://www.baysiderentalsnh.com/
You can search properties online and contact them and they will try to find you something even if it does not appear as available. Instead of relying solely on available/online searches they often reach out to us owners to see if there's a way to make it work. For example, our unit has been unavailable past few weeks due to renovations and they called to see if we could move things around for potential renter. We couldn't make it work since floors had been ripped up and were in process of being replaced but we appreciated that they called to verify that it was truly unavailable!