Collins says "cheerfully" has three meanings happily, unthinkingly, and unhesitatingly It seems that in the sense of "happily" or "unhesitatingly," the word "cheerfully" works as a VP adverb, while used in the sense of "unthinkingly" the same word now functions as a sentence adverbWhat is an Adverb?Filtred list of similar words for Cheerfully is here
Eng Remed 9