The marriage certificates I have viewed in my research have not included parents names unfortunately.
This is not peculiar to the IoM, I have 2 in New South Wales ,descendents of my still brick walled LYNCHEY, where the minister was notorious for running a "Marriage Shop" and the Presbyterian Archives in Sydney told me that "perhaps the Bride and Groom's names were correct and maybe the date"
He was apparently in the habit of marrying under age girls and people who were already married. For the fee apparently.

Cheers

Peter
Melbourne