The pattern is apparently called "peony" (some slight variations, i.e. pineys, paeony) and it is a variation of a Lemoyne Star block. Thanks to everyone who responded to my plea for help. It set me off on the right path to identify the block.
The Carolina Lily pattern that was suggested is very close, but it lacks the last 2 petals/leaves of a true Lemoyne Star/peony. The setting with the stems and vase are typical of the Carolina Lily, but the piecing is different. The leaves on the antique quilt are also pieced diamonds, not applique as most Carolina Lily patterns seem to be.