This word for the fur of a rabbit was rare in the 18th and 19th centuries then boomed again with the booming fur-trade of the later 19th century.  As a work-related word, we are tagging it as low, as Bilbo seems to do when at first trying to wrap his head around whether Beorn as a “skin changer” is a person of lower station than himself.

• 07.021 a man that calls rabbits conies,

“coney, n.1.” OED Online. Oxford University Press, March 2015. Web. 20 May 2015.