If you're looking for a type of coconut oil that works well to relieve constipation and provide good health benefits at the same time, I'd say the best coconut oil for the job is virgin coconut oil.
But if your definition for "best" is you desperately need a more potent type of coconut oil for the "difficult" task, MCT oil is for you.
MCT oil is a type of fractionated coconut oil. It composes solely of MCTs (medium-chain triglycerides). Virgin coconut oil carries about 50 – 64% of MCTs.
What makes coconut oil a good natural laxative? Its MCTs. Hence, the fractionated MCT oil works faster and stronger. But please start off with a teaspoonful or less as the stomach upset may be too strong for you to subdue. I still advise virgin coconut oil for constipation relief. Alternatively, RBD coconut oil if you prefer odorless.