There are various synonyms that can be used to describe "alternate bouts of depression and happiness." Some of the common synonyms include mood swings, emotional upheaval, roller coaster emotions, alternating state of mind, up and down emotions, and fluctuating moods. Other apt words that could be utilized in this context are bipolar disorder, manic depression, feeling of highs and lows, and chronic moodiness. Such words are often used to describe a person's emotional state and can be an indicator of a mental health condition that needs to be addressed. Though the words might not be the same, they all point to the same idea of alternating periods of sadness and happiness.