Boyishly tells you how someone does something: in a boyish way — like a boy, and usually in that attractive, open, slightly young way. He smiles boyishly; she grins boyishly; someone might shrug boyishly, as if the whole thing were light. It is the adverb that belongs with boyish, so it rides with a verb and describes the manner, not the person as a noun. The tone stays warm; you would not use it to scold someone for being immature — for that, people say childishly. Though actually the tidy pair is simple: boyish smile (adjective before a noun), smiled boyishly (adverb after a verb).