Hi Carrie!
Thank you for visiting the Moms Panel!
At both of Disney's water parks -
Blizzard Beach, and
Typhoon Lagoon - you can reserve premium beach chair spaces which include two lounge chairs, an umbrella, table, and two towels. You cannot reserve these in advance as they are only available on a same-day, walk-up basis. The cost for these is about $40 per day. From what I can remember they are located around the edge of the beach area.
If you wish for more luxury you can rent a premium space known as a Polar Patio. These include an attendant, refreshments (bottled water and all-day drinks mugs), towels, your own private locker, and more. Each shack accommodates up to six guests and costs around $250 per day.
For full details and to make a reservation call (407) 939 7529.
If you have any more questions, please come back and ask me - I would be happy to help you plan your magical vacation!