From the work that I have done I can find no crest or motto, traced back to England although I'm sure that one exist.However the meaning fo the name has been identified, see below.
The English surnames are, based on the first name of the mother or father.In this case, the surname Sibley is derived from the first name Sybil and simply signifies the daughter (son) of Sybil. This name Sybil is derived from the ancient Greek Sibyl, in mythology she was one of the priestesses who uttered the ancient oracles for the gods and who was later accepted as blessed with divine revelations, and admitted to the Christian heaven along with the prophets.
It is quite unusual for a female to be the progenitor of a family name, the explanation is that perhaps the mother of the initial bearers of this name was a more prominent figure in society rather than the father.If the mother was in fact descended from the ancient line of Priestesses of Cyble would be quite understandable.
This name was introduced in England after William the Conquerors son Robert married a girl called Sybylla and thus the name took root.
Variants of this surname include Sibly and Sebley all of which are quite frequent in Suffolk, Norfolk and Devon. An early recorded instance of this name occurs in 1275 when one Geoffry Sibilie is recorded in Suffolk (Rotuli Hundredorum). Another instance occurs in 1327 when one of Richard Sebeley is recorded in Suffolk (Subsidy Rolls).
Sibillia wife of Lombardo de Fraguliti from Vicomercato, Upper Lombardy (1384-1390). She was executed as a witch.
In America there is a reference to John Sibley, a church member from Salem in Massachusetts, in 1640.His wife Mary Goodwife Sibley made witch-cakes which she fed to the girls claiming to tormented by demons, in order for them to tell the truth!Knowing what might be coming they left for New Hampshire before the witch-trials began.