meaning of 才对 (cái duì)

Consider this pair of sentences giving in sequence.

这个颜色不对。(Zhè ge yán sè bú duì.)
这个颜色才对。(Zhè ge yán sè cái duì.)

The first sentence clearly means "This color is incorrect."  The second sentence seems to then mean "This color is correct."  What is the significance of 才?  Is it being used for emphasis?  Would a more accurate English translation be "this color IS correct" with us emphasizing it with our voice?  Would it also be ok to say

这个颜色对。(Zhè ge yán sè duì.)

where we omit the emphasis?
 

You are correct in assuming 才 is being used for emphasis. However, a better translation would be: this is the RIGHT color where you are presumably correcting someone for choosing the wrong color and placing emphasis on the word RIGHT. Pretty similar to using 就 but in this situation 才 would be the better choice.

The sentence 这个颜色很对 (Zhè ge yán sè hěn duì.) is a simple statement claiming this is the right color without emphasizing any word.

I hope this is of some help to you.

That is very helpful.  Your second sentence 这个颜色很对 (zhè ge yán sè hěn duì) makes good sense too, using 很 to connect the subject to the adjective.

你们好！

This is a convention in Chinese that isn't always that easy to explain in English because there is no 'one structure fits all' when it comes to translation. However, I will do my best to do so and as clearly as possible.
这个颜色不对。 As you pointed out, this simply means 'this is not the right colour'. (Note I didn't directly translate) As it stands this sentence can be its own stand alone sentence with not reference to any previous clause or context.
However, 这个颜色才对 is not. The word 才 (which in some cases can be translated as 'rather' as in 'this one, rather than that one') in this sentence alludes to the previous sentence and makes the clear distinction that unlike the previous colour, this colour is in fact the right one. If you were to translate the two sentences collectively, rather than separately you should get a clearer picture:

这个颜色不对，这个颜色才对。
This isn't the right colour, however/rather this one is.

I hope this helps and keep up the good work!

   -   Lin Ping