There's also reading sunglasses which are closer to sunglasses fitted to the eye, but they also have to plano or no power and can't be found cheap.
The average diameter of a cornea, and consequently the size of a contact lens, is 12 mm; of course I'm talking about a lens that is useful in blocking the sun and would go over the white of the eye, so for the whole eye I think that's doubled to 24 mm. I don't have a ruler on me, and most sunglasses are made to be bigger because that's in fashion. But the images of most commercial camera lenses can be googled in a variety of sizes, so I can look at the glass on them to get an idea of the size of a sunglasses lens if it was made. Right now I'm thinking that in the case of a circular lens I've been daydreaming about, it would be between 24 (which might be too small) and 32 millimeters width for the average person.
EDIT: I wrote up suggestions and sent them to a bunch of companies last night, so hopefully something cool will come out of it.