"On the up and up" is a common phrase used to indicate that something is honest, legitimate, and going well. Its antonyms are "on the down and down" or "on the decline." These phrases suggest that something is not going well, that it's becoming worse, and that its future is uncertain. Another antonym for "on the up and up" is "shady" or "suspicious," which implies that the situation or person in question is untrustworthy or involved in dishonest activities. Synonyms for "on the up and up" include "aboveboard," "legal," "honorable," or "righteous," which convey the sense of being honest, straightforward, and lawful.