Is there an item in a camera's specifications that can indicate the quality of color reproduction in that camera?
There are a lot of things you can find out about a camera before buying from reading the specs: pixels, zoom, sensor.
But there are some cameras that are taking images with terrible colors, and quite simple ones that are getting the accurate and real colors, and I would like to know how to tell these apart from the specifications.
I there a way to know that?
First, it's unclear to me what you consider to be "good colors". The quality of color reproduction is a complex chain of dependencies, such as white balance, filters, iso value (color noise), lens, color space, image format, monitor and printer quality, etc.
Second, most photography review sites (of which dpreview is my personal first choice) have a paragraph or two in their reviews about image quality. For example here is a link to such a page for my latest buy, a Panasonic Lumix LX100.
In the glossary of DPreview there is an interesting statement about color accuracy:
Conventional sensors using a color filter array have only one photodiode per pixel location and will display some color inaccuracies around the edges because the missing pixels in each color channel are estimated based on demosaicing algorithms. Increasing the number of pixel locations on the sensor will reduce the visibility of these artifacts. Foveon sensors have three photodetectors per pixel location and create therefore a higher color accuracy by eliminating the demosaicing artifacts. Unfortunately their sensitivities are currently lower than conventional sensors and the technology is only available in a few cameras.
Most digital camera review sites measure color-accuracy. This is measurable in comparison between the sRGB or AdobeRGB color-space and the JPEG output from a particular camera. Where you be careful is that most sites only measure the default settings while most digital cameras can be improved greatly with adjustments.
There is also a subjective component to judging colors and some reviewers will simply prefer colors from one camera or brand (which tend to choose a consistent rendition). For this, I would look online at image samples. There of course you must be careful to be looking at unaltered images and you must also have a reference point to know what the colors should be like.
A measurement of color accuracy is the sensitivity metamerism index. Numbers are available on the DXOMark website. Interpreting the numbers is another question.
The colour accuracy depends largely on the interpretation of the raw sensor data in software. When shooting JPEG, you're obviously at the mercy of the camera firmware, but if you shoot RAW, you can utilize different profiles in your converter software, and, for greatest accuracy, you can build your own custom profiles with a colour chart and appropriate software (I have no personal experience in this, so can't give details). In this case, you'll get accurate colour rendering, (largely) regardless of which camera you use.
Nearly all cameras use a similar Bayer pattern approach, and will have similarly reduced colour resolution, only the Foveon sensors mentioned above are different, and probably better, in this regard.
I there a way to know that?
Yes. Simply try the camera. Rent it, go to a shop that allows you to take sample images or try to find example images of the camera on the internet.
Please keep in mind that humans are also a big part of the chain of dependencies mentioned by @agtoever. Maybe the colors are off because the person who took them wasn't very good at that.
