You can use soy milk. Just make sure it's lactose free, in case it's the lactose the person is allergic to. There is also a great book called Vegan Cupcakes Take Over the World. Also beware of coffee creamers if you use those in your icing. They say that they are non-dairy but they still have a milk protein in them called cassein, which people could also be allergic to.
See this link for lists of milk derivatives that you'll have to look for in any ingredients you use:
http://web.mit.edu/kevles/www/nomilk.html#badingredients
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