Most people who drink BPC put in a tablespoon each of unsalted butter and coconut oil. I believe the reason is simply that the popularizer of the drink did it that way.
The satiating effect of BPC is greatest with two tablespoons of fat, whichever sort you choose. If it is merely the consumption if fat that concerns you then it hardly matter which you choose.
However, many believe there are greater overall health benefits in coconut oil, mainly that portion of it which contains medium chain triglycerides.