The standard Nativity places Mary and Joseph in the center of the action. While their story is important, put a twist in the tale by focusing the action around other characters. For example, the story features three wise men and three shepherds who come to visit Jesus. Rather than concentrating on how Mary and Joseph reach the stable, examine the journey of these other travelers. You could focus on angels in heaven, who observe the action and comment on it.
The stock characters of Nativity plays -- Mary, Joseph, the shepherds and the wise men -- don't have to be the only characters in the story. While Mary and Joseph are major characters, others characters can offer a new perspective and create more roles for others who want a part in the play. Mary and Joseph could stop to speak to more characters on the road, or other animals could turn up to watch the stable scene.
The biblical period is the setting for a traditional telling of the Nativity, but more radical plays can break away from this. Keep the birth of Jesus, the integral element of the story, as the focus but shift the action to a different setting. Reflect the setting in the play’s costumes, set designs and the music you use. For example, try a Victorian England setting, with chimney sweeps rather than shepherds and gentlemen in waistcoats rather than wise men. Alternatively, you could stage a modern interpretation. For example, the play's plot could feature kids from the 21st century who find a way to travel back in time to witness the Nativity.
Other interpretations of the Nativity scene can place the birth of Jesus at the center of the play, without featuring the scene in the stable. You can set such plays after the events of the night Jesus is born, with one character describing to another what has happened.