Hmmm. I'm not sure if there is a way to keep the custom listing private or not other than the request custom item (as Bev said).
I keep a custom listings section in my shop that is usually empty, except when I have a custom listing for a customer. That way people know its not for them. I do find that sometimes people are curious and click through anyway, but I figure that can't hurt as the real customer's user name is on the listing. Plus when people see what other people are buying maybe it will give them ideas of their own and more sales can be made from that - wishful thinking!