I am afraid that I am a bit sceptic, like my kins, when expressing or talking about happiness (there are always some little or bigger clouds on the sky - which cause some "buts" and "wait a minute" - lol), and we rather say "I am glad" or "I am sooooo glad" and speak more of satisfaction (contented), admiration, rejoicing, looking forward to a happy event, saying a hearty thank you, and of how much we appreciate and like somebody, a deed, a gift or a hilarious, "fantabulous" joke.
And sometimes, we are "sooooo happy" - but these very short moments cannot last. Furthermore one happens to be ironic or even sarcastic about being happy, a bit like Fernand Raynaud, rather upset in his famous sketch "Heureux !" ("Happy!"). Sorry, no translation found or done ...
We express or remember moments of happiness with a smile, tears, dancing, jumping, hugs, kisses, shaking hands, awkward moments, a silent bow, laughing and cheering, a prayer and a blessing, "hooray", "yippee", "oh joy", "halleluja", "aw", "whee", "hip hip hooray", "God bless you", "thousand thanks", "so cute", "yummy", "wow", "I'm so glad", "love it", "how wonderful", "that's fabulous", "you made my day", etc., etc.
They say more about feeling happy than saying the very words.
Droopy makes nearly always a sad face and says "I'm happy", or "You know what? I'm happy"!
Still, maybe that we should remember to say more often "I am happy" to express satisfaction and be more thankful for such wonderful moments ...