My kids are allergic to dairy and you can make almost all treats, including cookies, rice krispie treats using an organic Palm shortening (non-hydrogenated) or vegetable oil (for things like cupcakes).
Also, I suggest that you give all the kids the same treat (which I think you're are saying you plan to). It can be extremely socially isolating for these kids to be given something different. It's really important for kids to feel they're a apart of the group. I know this first hand is my boys are on a GF/CF (gluten-free/dairy free), so I try to make treats when I can (and now that they're older this is less of an issue other than pizza).
Even if the child is also allergic to eggs, you can make cookies using an egg replacer. But, I suggest something like the rice krispie treats which don't need eggs or dairy or most other allergens.
Finally, you are very kind to be so considerate. I can tell you that some folks are not at all and make no effort in this area. However, it is amazing the change in these same folks when one of their is diagnosed!