This is a dairy free recipe I tried recently and it was quite well-liked:
NGREDIENTS
* 3 cups all-purpose flour
* 2 cups white sugar
* 1 teaspoon salt
* 2 teaspoons baking soda
* 1/2 cup unsweetened cocoa powder
* 3/4 cup vegetable oil
* 2 tablespoons distilled white vinegar
* 2 teaspoons vanilla extract
* 2 cups cold water
DIRECTIONS
1. Sift flour, sugar, salt, soda, and cocoa together into a 9 x 13 inch ungreased cake pan. Make three wells. Pour oil into one well, vinegar into second, and vanilla into third well. Pour cold water over all, and stir well with fork.
2. Bake at 350 degrees F (175 degrees C) for 30 to 40 minutes, or until tooth pick inserted comes out clean. Frost with your favorite icing.
If you look it up on allrecipes.com, there are also a few variations without chocolate.
Happy Baking!
Sorry no recipes for cakes, but Cherrybrook Kitchens sells an assorment of Gluten-free, Dairy free, soy free cakes (they don't have yeast in most of them either)... you just have to read the labels to make sure which one you have.
Also, I use Spectrum's Palm Oil (coconut oil) Shortening in place of other shortenings that contain soy, if that's of interest for you.
Try http://www.cs.unc.edu/~kupstas/FAQ_recipes.html
Recipes for kids with allergies.
The recipe posted above is my all-time favorite chocolate cake recipe. Moist, dark and chocolatey, super easy to make--what's not to love? And with no eggs, no dairy, it's vegan as well as good for people with dairy allergies! It's called "crazy cake" and "wacky cake" that I know of, but there are probably other names for it as well.
I adapt it to make different flavors all the time. Replace the cocoa powder with flour and you have a white/vanilla cake. Make the white version and add strawberry puree and a box of strawberry jello and you have strawberry cake. Replace some of the water with orange juice concentrate and you have orange cake. Replace some of it with lemonaide concentrate and you have lemon cake. voilla. the only recipe you'll ever need. 
Martha Stewart had a lady on about a month ago that has a bakery and she did allergy free cupcakes also frosting I think this is what you are looking for. I wish I could tell you more.
I found it the lady that martha Stewart had on was Erin McKenna she owns a bakery in NYC called Babycakes. If you go to Martha Stewart.com you will find a few recipes I did not see her frosting but I know she made on on the show. You can always call her shop to see if you can get some help.
If you are not 100% certain that you can do a cake without any form of sugar (or any of this child's other allergens), I would turn down the order. Here's the reason.....
My daughter is DEATHLY allergic to corn (among many other things). Most people think "Ok...I just won't give her any corn-on-the-cob". Here lies the problem..... she can't have anything that is a derivitive of corn.....corn syrup, cornstarch, dextrin, maltodextrin, sucrose, glucose.....just to name a few. Almost anything processed contains corn (as well as toothpastes, soaps, etc). 90% of what is in your pantry contains corn products.
The same goes for sugar. Even though a label may not say "SUGAR", it could be a derivitive of sugar....and this child could react!
As a mother of a child with multiple severe food allergies, I just want to ask you to really, really, really do your homework before you say that something is 100% free of anything! It's just not worth risking a reaction.
Good Luck to you!!! And HAPPY BAKING!
Yeah, I agree with the PP. It sounds like you are really stuck. You could probably come up with something...but if she is VERY allergic to those things, I would hate to risk it and make this child sick.
As Momthreekids said, you'd be surprised what hidden allergens lurk in foods, and if you aren't familiar with them and their alternate names (milk is also casein etc)...my son is milk and soy allergic and we have to read, read, read the labels to make sure he doesn't get them. Soy is in everything too.
Splenda, fruit juices, etc will sweeten, but are not good if she reacts to those as well... I think at the least, mom needs to give you a list of things that she CAN eat.
Myself, I would be worried about making the girl sick and also my liability for that.
have to agree on this one - I can try, but I'd never state that the cake was 100% free of whatever substance they are trying to avoid. I'll show them how I make it (they can watch if they want), show them the ingredients, but at the end of the day it is their decision.
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