Umbrella rentals in Galveston?

Is there any where that you can rent beach umbrellas in Galveston that aren't already on a beach? My wife and I are going this weekend for our anniversary, and planned on going to Galveston Island State Park to spend some time at the beach (and do some fishing, since you don't need a license in a state park). We would like to rent a beach umbrella for the day, but all I can find are companies that have them out on certain beaches already.