I always make icing with POWDERED SUGAR, WATER or LEMON JUICE and ANY ARTIFICAL FLAVORING (like vanilla, mint, orange, almond, coffee.....) pretty much the same as many other mommies already responded.
If you want anything to fill the cake with or frost it with, you can make any flavored pudding with water or fruit juice depends on flavor you are trying to get (on 3 1/4cup water or fruit juice put 2tbs cornstarch, a little over 1/2cup of sugar and any flavoring (vanilla, strawberry, or none or add cocoa powder for chocolate flavor)).
Here are some more ideas:
Vegan Chocolate Frosting
1 cup cocoa powder
3/4 cup margarine, softened
1 tsp vanilla
1 cup maple syrup
I know you are just asking for icing recipe but I had some more tips that I thought anyone who has the allergy problems might find it useful so here it is:
How to replace eggs in some recipes
Commercial Egg Replacer:
Ener-G is an incredibly versatile and easy to use. Ener-G and other store-bought egg substitutes are relatively flavorless and work best in baked goods, such as cookies, muffins and cakes, and can also be used to bind ingredients together in a vegan casserole or loaf. Ener-G is vegan and certified kosher, but be sure to read the labels carefully on other brands, as some may contain egg whites.
Bananas and Applesauce:
Smash up or blend about a half a banana or 1/4 cup applesauce to use as an egg replacer in baked goods such as muffins, pancakes or yeast-free quick breads, such as pumpkin bread, and of course, banana bread! Bananas and applesauce add the perfect amount of thick moisture, like eggs, but they won't help your dishes rise or turn out light and fluffy, so be sure the recipe you are using includes a bit of baking powder or baking soda to help it rise if needed.
Tofu (for the ones that are not allergic to soy):
Tofu is the best way to substitute eggs in dishes such as a quiche, frittata or egg salad. The texture of silken tofu or crumbled regular tofu is surprisingly similar to boiled or cooked eggs when used in a similar recipe and, by adding a bit of mustard, turmeric or nutritional yeast to your dish to give it a yellow hue, your eyes will be tricked as well as your taste buds!
Other Substitutes like soda:
In a pinch, or with a good recipe, vinegar mixed with water or even plain run-of-the-mill soda can work as a decent egg replacer. For savory entrees such as a vegetarian casserole or a loaf, try using 2-3 tablespoons of bread crumbs or oats.
How to replace butter in recipes:
Margarine, oil(for 1/2cup butter 1/3cup of oil), applesauce, pureed prunes, mashed
bananas and pumpkin puree as well as baby food in a jar.