Hooded or covered boxes Hooded boxes are most suitable for timid cats who need more privacy. (petsmagazine.com.sg)
However other cats dislike hooded boxes because smells can get trapped in there and the hood can restrict a cat's movements if not large enough. (best-cat-art.com)
Here are some boxes, both manual and automatic, that come with covers, often referred to as hooded boxes: (cat-lovers-only.com)