Here are some options depending on the context you're using it in:
* Bliss: This word suggests a state of extreme happiness and contentment.
* Joy: A more general term for happiness and a feeling of great pleasure.
* Elation: This word implies a feeling of intense joy and excitement.
* Delight: A feeling of great pleasure and satisfaction.
* Rapture: A state of intense joy, ecstasy, and overwhelming happiness.
If you're trying to describe a specific situation, you could use phrases like:
* A state of pure joy
* Overwhelming happiness
* Unbridled joy
* A moment of pure bliss
Ultimately, the best way to describe "happily happy" will depend on the specific context and the feeling you want to evoke.