General:
* Tranquilly
* Serenely
* Quietly
* Calmly
* Gently
* Harmoniously
* Contentedly
* Leisurely
* Composedly
More specific:
* Idly (suggests a lack of activity)
* Placidly (implies a calmness that is undisturbed)
* Serene (suggests a sense of inner peace)
* Tranquilly (emphasizes the absence of noise and disturbance)
* Harmoniously (highlights the absence of conflict or discord)
The best synonym to use will depend on the specific context of your writing.