Green demon faces will rarely appear in rooms, usually on the later floors. If you have either 100 casings (money) or at least one curse from any source altars, cursed guns, stealing, breaking a mirror etc.), enter and to teleport to a market room with every item-selling Gungeon NPC available, including a side room with Winchester and his game. If you do not have 100 casings or a curse, the face will spit you out.