If you do something cheerily, you do it in a bright, happy way — you wave cheerily, you call out cheerily, you smile as you speak. It is the adverb from cheery: light happiness, a smile in the voice, not a deep or serious kind of joy. In everyday talk, many people say cheerfully or happily instead; cheerily is a little more old-fashioned and a little more like a storybook. Though actually, if a person is too cheerily bright when things are hard, it can sound as if they are putting a shine on a grey day.