Is there any material available that can quickly change its colour depending on some current applied to it? I want to build a display that does not emit light itself.
Yes, there are plenty of materials that change their colour when a current is applied to them, they are known as 'Electrochromic Materials'. Commonly, electrochromic materials are metal oxides, and have the ability to change, remove or heighten their colour when a current passes through them. 

This technology is already used in cars, mirrors and windows, and should work well with your display idea.