When searching for synonyms for the phrase "I can't tell you how happy I am," one could consider options such as elated, overjoyed, ecstatic, thrilled, or simply content. Each of these words conveys a sense of immense joy or satisfaction, and could be used in various contexts depending on the situation. "Elated" could be used to describe someone who has just accomplished a major goal, while "overjoyed" might be used to express how someone feels upon receiving good news. "Ecstatic" might be reserved for moments of pure bliss, while "thrilled" could be used to describe a state of excitement or anticipation. Overall, these synonyms offer different shades of happiness, each adding a unique perspective to the emotion being conveyed.