"Couldst do" is an archaic term that means "could do" in modern English. As such, antonyms for "couldst do" would be words or phrases that imply impossibility or inability. Such antonyms could be "can't do," "unable to do," or "incapable of doing." Other antonyms could include "forbidden to do," "prohibited from doing," or "not allowed to do." These antonyms convey a sense of restriction or obstruction that prevents someone from being able to do something. Ultimately, the antonyms for "couldst do" depend on the context and circumstances in which the phrase is used.