The word "give no credence" means to not believe or refuse to accept something. Some of the antonyms for this phrase are "believe," "trust," "accept," "embrace," "acknowledge," "recognize," "admit," and "affirm." When you "give credence" to something, you consider it valid or reliable. But, when you "give no credence," you cast doubt on it, and see it as false or untrue. Therefore, if you want to express your agreement with a particular idea or belief, you may use one of these antonyms in place of "give no credence." It all depends on the context and your personal perspective.