For general happiness and joy:
* Cheerfully
* Joyfully
* Happily
* Gladly
* Delightedly
* Lightheartedly
* With gusto
* With abandon
* With a flourish
For a lively and energetic tone:
* Briskly
* Spirited
* Energetically
* Vigorously
* Lively
* Animated
* With a swing
For a lighthearted and carefree tone:
* Carelessly
* Casually
* Frivolously
* Gaily
* Without a care
* With a smile
For a playful and mischievous tone:
* Mischievously
* Naughtily
* Waggishly
* Teasingly
The best synonym for "merrily" will depend on the specific context of the sentence.