It sounds as though you need a customer portal. There are several customer portal options available for CRM, including a free one, but I'm not sure that any of the available portals provide a customer-facing version of the CRM calendar. You can find them on PinPoint: pinpoint.microsoft.com/.../search
Please also note that if you are using CRM 2011 on-premise, that you'll need to buy a CRM external connector license before you can build or deploy a customer portal.
