1610s, perhaps from Dutch kooi "cage," used of a pond surrounded by nets, into which wildfowl were lured for capture, from West Germanic *kaiwa, from Latin cavea "cage." The first element is possibly the Dutch definite article de, mistaken in English as part of the word. But decoy, of unknown origin, was the name of a card game popular c.1550-1650, and this may have influenced the form of the word.
1650s, from decoy (n.). Related: Decoyed; decoying.