People have chimed in with all of these possibilities:
Walmart clamp umbrella
Toys R Us Radio Flyer umbrella with clamp
Toys R Us baby stroller umbrella with clamp
Kids or compact umbrella, cut off handle, pole slotted into clamp or duct-taped to stand
Golf club umbrella (
http://www.theclubumbrella.com/index.php)
REI Travel Chair Umbrella (with clamp)