You can collect car parts by beating the group of people who attack your settlement in the car. It's a random event that occurs when you click to go outside the settlement after a while. You can also buy them from the parts guy at the race track.
I think the quarry is in development but you can send guests to work there and collect and store the materials but they do get dissatisfied quickly and want the day off or may want to leave.
Thank you both, i'll keep a look out for it.You can also get car parts from the toxic cave exploration event. Requires a gas mask (on every single companion and yourself) to survive. It is not guaranteed, but one of the possible main rewards is a car part.