Booking in advance not only ensures a better chance of getting the vehicle of choice, it can save you up to 8% on your car rental. For a below average price, Cheapflights recommends booking your car rental at least 42 days in advance.
The length of time you can book a rental for is subject to the inventory of the supplier. When renting a vehicle from Big Island it should be possible to rent a car for a whole month if needed.