Definition from Wiktionary, the free dictionary
Perhaps an alteration of captain.
copatain (not comparable)
- (obsolete) Pertaining to a hat with a high pointed crown.
- O fine villain! A silken doublet, a velvet hose, a scarlet cloak, and a copatain hat! O, I am undone! I am undone! While I play the good husband at home, my son and my servant spend all at the university. — Shakespeare, The Taming of the Shrew, Act 5, Scene 1.