Simple:
* As happy as a clam
* As happy as a lark
* As happy as a puppy
* As happy as a kid in a candy store
More Descriptive:
* As happy as a butterfly flitting through a meadow of flowers
* As happy as a warm summer breeze
* As happy as a wave crashing onto the shore
* As happy as a sunrise on a clear day
Figurative:
* Happy as a songbird singing in the morning sun
* Happy as a ship sailing on calm seas
* Happy as a fire crackling in the hearth
* Happy as a star shining brightly in the night sky
The best simile will depend on the specific context and the desired effect.