For each egg you are replacing mix together 1/2 teaspoon of baking powder, one tablespoon of white vinegar and one tablespoon of water. After combining the mixture add it to your recipe. This works great in cookie dough batters as well as other recipes.
There are some cookie recipes out there that don't call for eggs. There is the no bake cookie that is just peanut butter, chocolate, and oatmeal. I have found a great sugar cookie recipe that you might like also. Here is that link. http://www.cooks.com/rec/view/0,1916,152181-243198,00.html
For the few cookie batches I've successfully made yummy and vegan-flax seeds worked well! Crushed and whisked with water, they are gooey as heck. from the PostPunk Kitchen: "How to use it: 1 Tablespoon flax seeds plus 3 Tablespoons water replaces one egg. Finely grind 1 tablespoon whole flaxseeds in a blender or coffee grinder, or use 2 1/2 tablespoons pre-ground flaxseeds. Transfer to a bowl and beat in 3 tablespoons of water using a whisk or fork. It will become very gooey and gelatinous, much like an egg white. In some recipes, you can leave the ground flax in the blender and add the other wet ingredients to it, thus saving you the extra step of the bowl. "