From The Collaborative International Dictionary of English v.0.48:
Cony \Co"ny\ (? or ?; 277), n. [OE. coning, conig, coni, OF. connin, conin, connil, fr. L. cuniculus a rabbit, cony, prob. an Hispanic word.] [Written also coney.] 1. (Zool.) (a) A rabbit, esp., the European rabbit (Lepus cuniculus). (b) The chief hare. [1913 Webster]
Note: The cony of Scripture is thought to be Hyrax Syriacus, called also daman, and cherogril. See Daman. [1913 Webster]
2. A simpleton. [Obs.] [1913 Webster]
It is a most simple animal; whence are derived our usual phrases of cony and cony catcher. --Diet's Dry Dinner (1599). [1913 Webster]
3. (Zool.) (a) An important edible West Indian fish (Epinephelus apua); the hind of Bermuda. (b) A local name of the burbot. [Eng.] [1913 Webster]
From The Collaborative International Dictionary of English v.0.48:
Chief hare \Chief" hare`\ (Zool.) A small rodent (Lagamys princeps) inhabiting the summits of the Rocky Mountains; -- also called crying hare, calling hare, cony, American pika, and little chief hare. [1913 Webster]
Note: It is not a true hare or rabbit, but belongs to the curious family Lagomyid[ae]. [1913 Webster]