* χαρούμενος (charoumenos): This is a good general word for "happy" or "joyful," often used to describe a feeling of cheerfulness and lightheartedness.
* ευτυχισμένος (eftychismos): This translates more to "lucky" or "fortunate," implying happiness derived from good fortune or a positive situation.
* ευδαίμων (eudaimon): This word is more philosophical and signifies a state of flourishing or well-being, encompassing happiness, prosperity, and virtue. It's a deeper, more lasting kind of happiness than simple cheerfulness.
The best word to use will depend on the context.