Starting Menu Book 4 will unlock the Tuning Shop.
I simply went there, toggled to the Club Sports tab, and down the bottom were Dirt Tyres for a little over 4,000 CR (i can't remember exactly), and the trophy popped (:
You can, obviously, buy anything you wish, the cheapest being Sport Brake Pads at 400 CR, but as i needed dirt tyres for another trophy, it only made sense