I don't really like nickname-names. I love nicknames, but prefer them to be a term of endearment or something that the older sibling came up with, or something that just fits them perfectly or randomly happened. The nickname chooses you, I firmly believe.
But ... I just ran across Cricket and thought that would be such an adorable nickname on a little girl.
Ellie (Elisabeth, Eleanor, etc.)
Annie (Annemarie, Anneliese)