Generally, for a better deal at Pago Pago Airport it’s recommended to book in a timely manner (to save up to 20%). Cheapflights recommends you book around 71 days prior to your pickup date. Booking as early as you can also increases the likelihood that you’ll get the ideal car.
Typically, how long you can hire a car for depends on the inventory of the supplier. For Pago Pago Airport however, it is certainly possible to rent a car for an entire month.