Presumably the customer wants to contact you in situations where you shouldn't necessarily be contactable -- outside of office hours, or on personal time.
Unless you work in a time sensitive field, where real emergencies need to be addressed immediately, I'd be pretty firm on this one.
Managing Customer Service Expectations Is Important
It's important to send a message that while you value the customer, you can't be at his or her beck and call. You aren't going to say that specifically, but here's an example of how to say no.
"John, if you use the standard office number, even if I'm away, I check it every six hours or so, and I can promise you I'll get back to you within that time span. If you have something urgent, I can give you a company emergency number".
As is the case with having to refuse any customer request, try to offer something before you refuse the actual request.