The phrase "cop some z's" is a commonly used slang term that means to get some sleep or take a nap. Antonyms for this phrase could include terms such as stay awake, remain alert, or avoid sleeping. Other antonyms may include phrases such as cut back on sleep or reduce rest time, which indicate a deliberate attempt to get less sleep than usual. Overall, there are many different antonyms that may be used to describe the opposite of "cop some z's," depending on the specific context and meaning of the phrase.