General synonyms:
* Slowly
* Leisurely
* Deliberately
* Calmly
* Gently
* At ease
* Without haste
* In a relaxed manner
* At a relaxed pace
More specific synonyms:
* Methodically: Implying a systematic and careful approach.
* Thoughtfully: Implying careful consideration.
* Gradually: Implying a slow and steady progression.
* Tranquilly: Implying a peaceful and serene atmosphere.
* Serenely: Implying a calm and peaceful state of mind.
The best synonym will depend on the context of your sentence.