In my country (Iran), the reference to blue, green, and hazel eyes translates exactly to "colored eyes" in English. However, I am not sure whether the phrase "colored eyes" would be perceived and understood in English the way it is in Iran, and to be honest, I personally think it’s wrong to use that phrase in any language since that would make black and brown eyes "colorless". But is there a word specific to bright-colored eyes?
Use "Light-colored eyes"
As a native (American) English speaker, this would certainly convey "not brown or black". It may also exclude certain dark greens, which I’m not sure if the original Iranian phrase would.
Note that below some of the images are out of context, and appear to be used for comparison to dark eyes. I did not attempt to filter them out.