Although the natural colour of rubber is a milky white, the black colour we see was originally caused by soot. The soot was thought to increase the durability of the tyre along with cotton threads, which were inserted in order to reduce heat and increase stability. However, the main reason for black tyres on cars today, is the chemical compound ‘carbon black’. It is used as a stabilising chemical, which is combined with other polymers to create the tread compound of a tyre. 

The black color of tires comes from carbon black, a readily-available material that provides greatly improved wear characteristics and heat-dissipation capabilities when added to rubber compounds. Natural rubber is off-white in color, and in fact the first rubber tires were white.

As previously said, Carbon Black adds desirable properties to "rubber" used in tyres.  French bicycle tyres used to be made of butyl rubber and they were red.  I suppose any colour pigment you wished could be added to the process - at a cost.  Most purchasers are conditioned to expect black tyres at the lowest price and most tyre manufactures are conditioned to produce them that way...

And occasionally manufacturers go through a trend of differentiation such as the use of a "white wall" (decorative contrast color applied to the side surface of the tire). These were quite stylish on early Buicks etc. I think any manufacturer who tried to bring back a white wall tire today would be ridiculed.