I found the Baptist Orphanage in 1920 Hinds County, Beat 1, Street address Livingston Road. However, as I recall it was bounded on the West by Livingston Rd, on the East by Bailey Ave. and on the South by Asylum Rd. I don't know when it became part of the city.

There are several ways to reference census pages:
NARA method, T625, roll 878, pg (stamped) 31 A & B and 32 A & B
or Hinds County, ED 2, Sheets 18 A & B and 19 A & B.
I hope to attach the 1925 Sanborn map for the orphanage.