Instead of eggs, try...
Pureed pumpkin. Whether you're baking sweets or making a savory dish that calls for an egg as a binding agent (such as meatballs), Celine Steen, who blogs about vegan cooking at Have Cake Will Travel, says you can use pumpkin puree instead. She knows the squash may seem out of place, but promises you can't detect the flavor—and you'll be rewarded with moist, light baked goods—or even meatballs (vegetarian or not). Use about a quarter-cup of puree to replace/as a substitute for each egg.