Hi Danielle,
Premium Beach Chair Spaces are available to rent at both of the Disney Water Parks and include 2 lounge chairs, umbrella, cocktail table and 2 towels. (Limit is up to four people.) These are called Lodge Picnic Umbrellas at Disney's Blizzard Beach Water Park and Getaway Glen at Disney's Typhoon Lagoon Water Park.
Although it is a few years old now, there is a post on the Disney Parks Blog called
Enjoying Polar Patios at Disney's Blizzard Beach Water Park which provides information and photographs of the Lodge Picnic Umbrellas - Premium Beach Chair Spaces. This should give you an idea of what you can expect if you do decide to go ahead and book a Premium Beach Chair Space.
I would also recommend that you take a look at the Typhoon Lagoon FAQ section of the unofficial website AllEars.Net (http://allears.net/btp/faq_tl.htm) to give you an idea of costs (please do however bear in mind that prices are always subject to change).
Reservations can be made up to 180 days in advance by calling 001 (407) WDW-PLAY or 001 (407) 939-7529 from here in the UK. When I have to call the USA to pre-book anything for our upcoming visits to the Walt Disney World Resort, I always call via Skype to ensure that costs are kept to an absolute minimum.
It is also possible to book a Premium Beach Chair Space on a walk-up basis once you arrive at the Water Parks although availability cannot always be guaranteed.
Full payment is required when making a reservation. Should you wish to cancel, you must do so before 9:00 AM the day before your reservation.
Wishing you a magical holiday filled with memories which will last a lifetime!
Emma