What is the adverb of happiness?

Happy is an adjective. The adverb form is happily. The comparative adverb form is more happily, and the superlative is most happily.

When a comparative has two syllables as in happy, in most cases it can be used two ways (1) happier, or (2) more happy. Either way is correct. However, the -LY adverb forms must use "more" and "most" to express the comparative and superlative.