You could try to convey the sound through:
* Onomatopoeia: Words that imitate sounds, like "whee!", "yay!", or "giggle."
* Descriptive words: Words that paint a picture of happiness, like "joyful," "lighthearted," or "contented."
* Music: Music can evoke strong emotions, including happiness.
Ultimately, how you spell the sound of happiness depends on your own personal interpretation.