Android does not offer a native way for contacts' birthdays to be shown in the calendar - at least not for non-Google accounts.
One possible solution is Birthday Adapter by Dominik Schürmann. It provides a calendar with all contacts' birthdays which can then be displayed in all calendar applications using the standard Android calendar API.
Depending on your device it might be necessary that you use a specific date format when you add a birthday to a contact. These formats can be found on the following page; http://dmfs.org/carddav/?date_format