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]

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]

WordNet (r) 3.0 (2006):

cony
    n 1: any of several small ungulate mammals of Africa and Asia
         with rodent-like incisors and feet with hooflike toes [syn:
         hyrax, coney, cony, dassie, das]
    2: small short-eared burrowing mammal of rocky uplands of Asia
       and western North America [syn: pika, mouse hare, rock
       rabbit, coney, cony]
    3: any of various burrowing animals of the family Leporidae
       having long ears and short tails; some domesticated and
       raised for pets or food [syn: rabbit, coney, cony]