There are many different synonyms that one could use in place of the phrase "arrant coward," each with its own unique connotation. Some possible options might include "yellow-bellied," which implies a lack of courage or backbone, "timid," which suggests a fear of taking risks or standing up for oneself, or "craven," which implies a complete lack of bravery or courage in the face of danger. Other possible synonyms could include "milksop," "mouse," "wimp," "pansy," "weakling," or "sissy," depending on the tone and context in which the phrase is being used.