Is it possible to change eye colors without contacts or corneal surgery?

No: Eye color is the color of the iris, which is inside the eye, behind the clear cornea. The color cannot be changed, but colored contact lenses or colored implants (for patients missing portions or the iris) can make the eyes appear a different color.

Not really: The iris, behind the cornea, determines the color of your eye. There are some drops used to treat glaucoma that can change green eyes slightly more brown.

Not safely: There is at least one person in another country that I have heard of who puts in iris implants for purely cosmetic reasons, but there a lot of complications associated with this.