"Cheerfully" is an adverb, describing how something is done. Adverbs don't typically have comparative forms like adjectives do (e.g., "big" -> "bigger").
Instead of using a comparative form of "cheerfully," you can use:
* More cheerfully (This emphasizes a higher degree of cheerfulness)
* With more cheer (This emphasizes the feeling of cheerfulness)
* More brightly (If you want to emphasize the outward expression of cheerfulness)
* More enthusiastically (If you want to emphasize the energy of cheerfulness)
For example:
* Original: She greeted him cheerfully.
* Using "more cheerfully": She greeted him more cheerfully than usual.
* Using "with more cheer": She greeted him with more cheer than usual.
The best choice will depend on the specific context and what you want to emphasize.