This lovely set of 5 pieces is the "Coral" pattern, designed specifically for the Illinois Central Railroad by the E.A. Hinrichs & Company and produced by the Syracuse China Company, New York. Since it was for Railroad use only, it never carried a railroad marking, only the back-stamp of the Syracuse China Company.
The simply, yet elegant pattern consists of an airbrushed salmon pink background with creamy white floral design and flat rims. The pattern was first purchased for its named train "City of Miami" in 1935 and became the ICRR standard pattern until Amtrak took over. "Coral" was used on the "Panama Limited" and "City of New Orleans" named trains to accompany the "Pirate" pattern dinner plate.
The pieces in this set are: 7 1/4" plate, dated 1970; 5 1/2" plate, dated 1965; Saucer for cup, dated 1956; Cup, dated 1957 and 5 1/8" bowl, dated (I think) 1955. Each piece is stamped "Syracuse China (Date Code) U.S.A." There are no cracks, chips or repairs; near mint.