General:
* Chuckling
* Giggling
* Beaming
* Grinning
* Smiling broadly
* Chortling
More energetic:
* Whooping
* Hooting
* Guffawing
* Roaring with laughter
More lighthearted:
* Tittering
* Snickering
* Squealing with laughter
More joyful:
* Rejoicing
* Exulting
* Jubilant
The best synonym will depend on the context of your sentence and the specific emotion you want to emphasize.