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.
thanks for the info! do you know what is the general price range of these materials?
The cost can differ alot, but you could calculate with about 60USD per square meter.