The COE already demonstrated clearly that even with high taxes it is not going to stop people from buying cars.
the idea of a carbon tax is linked with the idea of externalities, and the economic reasoning that a positive and negative externality should be included in the price, i.e. the social marginal cost is higher/lower than that of the production cost.
to understand it more clearly, you can think of cigarettes as a negative example, and education as a positive example. when person A consumes cigarettes, person B, person C, person D around him are experiencing passive smoking. short of segregating smokers in their own little fishbowl space helmets, the additional negative impact that cigarettes bring to society should be included in their price. the idea is not dissuasion per se (of course, there is that additional impact), but to ensure that only people who are willing to pay the higher social marginal cost will buy cigarettes.
similarly, when people do things that produce carbon (whether it is driving a car, using electricity), this contributes negatively to society, on top of the raw materials that go into ensuring that such things can be done. the carbon tax merely tries to attach the externality and "price" it, such that optimal consumption is attained.
i'm not very clear on what the intention of the government was when they introduced the COE, but i'm quite sure that it has nothing to do with externalities, but rather an attempt to introduce a hurdle to curb demand. so the two (carbon taxes and COE) really shouldn't be lumped together, since based on my understanding, the basis of each is different.