General Happiness:
* Joyful
* Cheerful
* Glad
* Delighted
* Content
* Pleased
* Elated
* Jubilant
* Thrilled
* Ecstatic
More Specific Feelings:
* Contentment: Satisfied, at ease
* Excitement: Thrilled, eager, enthusiastic
* Joy: Delight, bliss, rapture
* Gratification: Fulfillment, satisfaction
* Bliss: Ecstasy, euphoria, heaven
Informal Language:
* Tickled pink: Extremely pleased
* Over the moon: Very happy
* On cloud nine: Extremely happy
* In seventh heaven: Extremely happy
The best synonym for "happy" will depend on the context of your sentence and the specific emotion you want to convey.