I think not all of the children are identified (there is a scrawled list on the back of the photograph), but here are the names that are known. (Feel free to leave a comment if you know who the children are.)
Patsy Williams played Mary.
Charles Scott (as an adult, he became Rev. Charlie Scott) played Joseph (standing).
Other children: Lynn Hill, Betty Williams, Agnes Giles (probably some of the angels), and Jerry Archer, David Leigh, Henry Law.
Children in the back: Malcolm Woodson, Michael Harris, Lillian Scott, Johnny Ray Neal, Susan Marsh, Carolyn Roach, Irene Barker, Michael Motley, Tom Hodgin, Terry Moore, Kenny Geyer, Wanda Sue Roberts.
Probably in the very back row: Randolph Barker, Jean Shanaberger, David Roach, Debbie Younger, Jane Worsham, Sharon Taylor (hard to read, could be a different name).
From the Preston B. Moses collection. Special thank you to the Moses family for sharing this picture.