You can generally use any type of coconut oil to clear acne except for the hydrogenated type. Even though coconut oil has only about 8% unsaturated fats to be hydrogenated, it's still unhealthy for the skin as the small amount of trans-fatty acids produced is still pretty damaging especially when it gets accumulated over time.
That said, you should use the most natural form of coconut oil like virgin coconut oil to treat acne effectively.
Virgin coconut oil carries medium-chain fatty acids (about 60%) that can penetrate deep into your skin to fuel cells so that they can expel toxins out of your skin.
Toxins are what make your skin dull and dispirited. Toxins also contribute to forming the plug that clog the pores.
Virgin coconut oil also holds about 90% saturated fatty acids, which can help to prevent further skin damage caused by free radicals. And all 10 fatty acids that are naturally present in the oil possess potent antimicrobial properties that can help to re-balance the acne bacterial count so that your skin will return to its healthy state.
Note that some brands (and companies) label virgin coconut oil as extra-virgin coconut oil. The names are different, but the method they use to extract the oil is essentially the same – cold-pressed. Meaning, extra-virgin or virgin coconut oil are actually the same thing.
Of course, different brands may produce varying quality of virgin coconut oil.
You can also buy a type of refined coconut oil that contains almost the same skin and health benefits as that of virgin coconut oil but without the odor. This kind of coconut oil, we call it RBD (refined, bleached and deodorized). It's thinner and so it can penetrate your skin relatively faster and of course, good for acne treatment.
Fractionated coconut oil (or liquid coconut oil) is another type of refined coconut oil. But it generally carries only caprylic and capric acids, which apparently have limited benefits for treating acne.
Of course, if fractionated works for you then just stick to using it. If not, buy either virgin or RBD coconut oil.
For your info, virgin coconut oil has a natural coconut scent whereas RBD coconut oil is odorless. If you don't like your skin to emit coconut odor, RBD coconut oil is the best for you to apply for acne treatment.
Last but not least, if you're always constipated, then besides topical application, you can actually consume virgin or RBD coconut oil to relieve constipation. Less toxic waste staying inside your body means less toxins will get stored in your skin. This definitely will help improve your acne and make your skin less acne-prone.