Sure, and there have been. Some municipalities have laws against them as the coloured streaks left on the road by spinning tires and hard braking get confused with other road markings, so, except for specialty use, there is no market for tire makers to make coloured tires. Besides, coloured tires are not as good as black tires.
Carbon black, for obscure reasons, something that Mr Goodyear discovered by accident, greatly improves wear resistance, and coincidentally, wet traction. It does not make the rubber harder or softer as such, but improves both wear and traction.
Coloured treads do not contain carbon black or they would be black, because the amount of carbon is substantial (over 25%).
Kumho makes coloured smoke tires, DOT-approved, for competition use only. There are multi-coloured motorcycle tires available for show bikes, again, not street use.