General Happiness:
* Joyful
* Cheerful
* Delighted
* Glad
* Pleased
* Content
* Elated
* Jubilant
* Exuberant
* Thrilled
Happiness with a specific cause:
* Grateful
* Thankful
* Satisfied
* Fulfilled
* Ecstatic
* Blissful
Happiness as a state of being:
* Serene
* Peaceful
* Tranquil
* At ease
* Euphoric
Informal words:
* Merry
* Chuffed
* Tickled pink
* Over the moon
Words that express a lack of sadness:
* Cheer up
* Brighten up
* Lighthearted
The best word to use depends on the specific context and the nuance you want to convey.