In fact, both coconut oil and olive oil are good natural laxatives for constipation. But when you compare their composition plus the experience that most people have, coconut oil performs better in relieving constipation.
The key difference between coconut oil and olive oil is the presence of MCTs (medium-chain triglycerides) in coconut oil. MCTs are able to digest in our stomach and break down faster into compounds that stimulate bowel movement. Which makes the laxative effect of coconut oil even faster and stronger than that of olive oil.
However, if you feel olive oil works well for you in this aspect, I don't see why you need to switch to coconut oil. Unless you want to reap the enormous health benefits from coconut oil besides relieving constipation.