General Happiness:
* Joyful
* Cheerful
* Delighted
* Glad
* Pleased
* Content
* Elated
* Jubilant
* Thrilled
* Exuberant
* Merry
* Blithe
* Lighthearted
* Euphoric
Specific Types of Happiness:
* Contentment: Satisfied, fulfilled, at ease
* Joy: Excitement, rapture, delight
* Pleasure: Gratification, enjoyment, satisfaction
* Bliss: Perfect happiness, ecstasy, euphoria
* Euphoria: Extreme happiness, overwhelming feeling of well-being
Informal Terms:
* Tickled pink
* Over the moon
* On cloud nine
* In seventh heaven
Words that Convey Similar Feelings:
* Optimistic
* Positive
* Upbeat
* Hopeful
* Enthusiastic
* Animated
* Lively
The best synonym for "happy" will depend on the specific context.