I think the comment from Shirley back in Nov of '03 is significant:

object made of a curved metal wire with a wooden handle. From the wire were suspended a dozen or so little white beads made of coral, fashioned to look like bell-shaped flowers. It looked just like a lilly-of-the-valley stalk. The label said something like, "Coral Bells: Used in the Colonial Period as a baby's rattle

so the lines

White coral bells, upon a slender stalk,
Lilies-of-the-valley deck the garden walk

rather then describing the colour of the plant 'coral Bells' are comparing the flowers of the lily of the vally to bells made of white coral.

The other item is that 'Coral bells' has traditionally been used more as a foliage plant then a flowering plant AND the pink and red flowering varieties were favored where they were used as flowers.

Then add in that the common name for the plant until recently was "alum root" and I think that evidence that the lines are referring to a single type of plant start to add up.

The age of the lines, however are still unclear. But I doubt if older then late 1700's