As you don't have any eggs the following are decent alternatives.

1. Applesauce: Substitute each egg with 1/4 cup of unsweetened applesauce. This will add moisture to the cake and help bind the ingredients together.

2. Yogurt: Substitute each egg with 1/4 cup of plain yogurt. This will add moisture and tanginess to the cake.

3. Buttermilk: Substitute each egg with 1/4 cup of buttermilk. This will add moisture and tanginess to the cake, as well as help with leavening.

4. Vinegar and baking powder: Mix 1 tablespoon of white vinegar with 1 teaspoon of baking powder, and substitute each egg with this mixture. This will help with leavening and binding.

You can follow the rest of the recipe as usual.
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