This can be done in either career or freeplay. The targets appear to spawn in a set order, but I found larger maps to be easier since it lessens the chance of the AI being right next to them when they do appear. In my experience they tend to hit the first ones very quickly but become worse as the game progresses, so don't be disheartened by a poor start.
By far the easiest car to use is Stella Stunner's since it will electrocute anyone within range, meaning you don't have to worry about hitting the peds directly. You can't steal it until chapter 15 though, so if you're struggling with these missions don't worry about getting them straight away. Remember to abuse the auto recovery (
) if you're about to crash, get pushed into a wall or go off the map. The credits you use will be more than balanced out by the ones you save having to use in repairs.