Here is the list of eggless cookies that I tried and came out good. All these cookie recipes without eggs have step-by-step procedure with pictures.
How to substitute eggs in Cookies?
In rare cases, vinegar too works in cookies.
Unsweetened applesauce will make the cookies very soft.
My favorite is Ener-G. Follow the directions given in the pack. For each egg to be replaced, you will have to use about a teaspoon of the egg replacer powder whisked with 3 tablespoons of preferably warm water. You can replace up to 4 eggs using this ratio.
Sometimes I even use about 1.5 to 2 teaspoons of Ener-G as the pack reaches the expiry date.