If its a puppet, you can't starve it, since you don't control the citzen allocation. But even if you could, you wouldn't want to. Building a courthouse is like building any other building, it requires production points, so the smaller the city, the longer it would take. Its true that you'll get slightly less unhappiness from adding a smaller city to your empire, but you're almost always going to be better off waiting for the city to be large enough that you can build a courthouse relatively quickly.
Other ways to help build the courthouse are to leave the city as a puppet until it is done rioting, make sure that you have enough happiness that you won't go below -10 (which gives you a huge production penalty), have workers ready to chop any forests that might be in range, and if possible trigger a golden age to get a production boost. It is also possible to purchase the courthouse building now, but it is still very expensive to do so, so it should only be a last resort.