The Collaborative International Dictionary
Copatain
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.]
A copatain hat made on a Flemish block.
--Gascoigne.
Wiktionary
copatain
a. (context obsolete English) Pertaining to a hat with a high pointed crown.