Before figuring out recipes, what foods CAN he have? Is he OK with eggs? Egg yolks can be used in a recipe if he's sensitive to only the whites (or if whites haven't been introduced yet). What juices does he tolerate well? Can you pump milk to bake with? Can he have wheat?
I think that you'd do better with a "muffin" type recipe, baked in a cake shape. In general, rice milk can be used in place of milk in any recipe- I've also had success substituting juice or even plain water in many recipes.
For icing, I usually just mix powdered sugar with butter (or any other solid oil, such as coconut, palm, non-hydrogenated margarine,etc.) and mix it until it looks right, then add a dab of vanilla. I don't know if that would be too high in sugar for you (maybe if there was no refined sugar in the cake and all the sugar was in the icing?)
You could also try experimenting with recipes ahead of time to see what he enjoys and agrees with him.