While there are a number of "almost" black paints you can buy, I generally mix my own. I add either a little flat white or flat tan to the flat black. Each model then has a unique shade on the tires, but so what, that is what real life is. Go out and take pictures of tires, you will find each car (or plane or whatever) has a somewhat unique color.
Only cars in a show, which have had a fresh coat of "tire paint" are ever really black.
In fact, I reserve real flat black right from the bottle for duplicating "openings". All else- real surfaces- I add some lightness too.