Use an acceptable vegetable pureed to replace the egg.  Some groups allow baking powder or soda, while others do not, but if you are one who does, add an extra 1 tsp of baking powder plus 1/2 cup of pureed sweet potato, carrot or squash in place of each egg.

If you don't use baking powder at this time, replace the liquid in the cake with sparkling water or have denser cake.

Pureed vegetables work as the best egg replacer I have found yet for egg allergic people.

BL