"Coral Bells" is the type of flower (Heuchera). They come in several colors, including white.
Lily of the valley is a different flower, but shares the bell-like shape. Isn't it clear that the exuberance of the melody and lyrics points to the excitement of seeing TWO kinds of bell-flowers, noticing their delicate little bell-shapes, and thinking of them as part of the fairy-world? (Lots of fairy drawings show them drinking from lilies of the valley, using them as bonnets, as bells, as bowls, etc. Their tiny delicacy makes them seem like a big white flower bell that was miniaturized.)