For, you saying the word 'Shy' it would be Shyly. As, 'She shyly smiled'. 'Shiley' is a name. The word 'Shyley' means to describe someone as an amazing, wonderful person. Calling someone a 'Shyley' is an act of kindness. As, 'Oh, shes such a shyley!' And 'Shily' is just a less common spelling of Shyly.
