General happiness:
* Smile
* Laugh
* Grin
* Beaming
* Rejoice
* Exult
* Celebrate
* Revel
* Thrill
* Cheer
* Jubilate
More specific feelings:
* Giggle (childlike happiness)
* Squeal (excited happiness)
* Chortle (deep, rumbling laughter)
* Bask (enjoying the feeling)
* Flourish (thriving, feeling good)
* Glow (inner happiness radiating outward)
* Exuberate (overwhelming happiness)
Verbs related to actions:
* Dance
* Sing
* Jump
* Skip
* Whirl
* Soar
* Leap
* Embrace
These are just a few examples, and the best verb to use will depend on the specific context.