The Coach Signature and Mini Signature Collections are crafted in signature jacquard fabric that has been specially treated to be water and stain repellant. To remove stains, simply wipe with a soft, damp cloth. It should not be treated with Coach Leather Care products.
Make sure the baby wipes don't have anything weird like shea butter in them. I use the Pampers Newborn Sensitive Wipes, where all they have is a touch of soap, and they work beautifully on my fabric bags.