The Collaborative International Dictionary of English v.0.48:

Copatain \Cop"a*tain\, a. [Formed fr. cop, in imitation of
   captain. See Cop, Captain.]
   Having a high crown, or a point or peak at top. [Obs.]
   [1913 Webster]

         A copatain hat made on a Flemish block.  --Gascoigne.
   [1913 Webster]