I've done both lemon and grapefruit juice, and the grapefruit juice is easier to handle than lemon juice. I think it's great to try new things, though, and my last flush was with LJ so... I mix the LJ and OO. My first experience with the flush was from a naturpath and that's what he said to do so I do it that way. I also follow up with lemonade.
I don't know about cocunut oil, but some people say do sunflower oil as it doesn't have as much linoleic acid as olive oil. Sunflower seeds have wonderful properties so I'd try that before coconut. Coconut oil goes rancid pretty quickly.