General happiness:
* Joy: This is a strong and intense feeling of happiness.
* Bliss: This implies a state of perfect happiness and contentment.
* Contentment: This is a feeling of satisfaction and peace.
* Cheer: This is a lighthearted and cheerful feeling of happiness.
* Euphoria: This is an intense feeling of happiness and well-being.
More specific happiness:
* Delight: This is a feeling of great pleasure and joy.
* Exuberance: This is a feeling of lively and enthusiastic happiness.
* Rapture: This is an overwhelming feeling of joy and ecstasy.
* Jubilation: This is a feeling of great joy and triumph.
* Beatitude: This refers to a state of perfect happiness and peace.
The best noun to use will depend on the context of your writing or conversation.