The short chain fats in coconut oil are supposed to produce ketones anyway so I don't see how that would be a problem. Jaminet recommends fats and fiber during a fast so an avocado might be all right, not sure though. I guess you just need to ask yourself, is what I'm about to eat mostly fat and/or fiber.

i'd go for the coconut butter. i almost never do coconut oil straight anymore, i loooove artisana's coconut butter though, and probably could eat a whole jar in a sitting...i think there are only 2 net carbs in a serving. (7 carbs, 5 fiber) or something like that.

i believe avocado has more carbs.

Keep the avocado portion small (like 1/2 a Hass avocado) and you should be fine. Also, you can mix a small amount of coconut butter into the coconut oil to improve its palatability, eliminating the chance of consuming too much coconut butter and knocking yourself out of ketosis.

If the coconut milk was pure (no guar gum or other additives) small quantities should be ok as well.

Are you including macadamia nuts in your fast? In Atkins (the chapter devoted to the Kekwick "fat fast") he seems to think that they are fine for deep ketosis. Also, egg yolks, some small amounts of fatty beef (~2oz) and avocado (the aforementioned 1/2 portion).

Here is a great post about what makes a diet ketogenic.... To quote from it:

So we have three ways to make the diet ketogenic:

1) Make Wilder’s “ketogenic ratio” high by eating a lot of fat, very few carbs, and not too much protein.

2) Supplement with the ketogenic amino acids lysine and leucine.

3) Supplement with coconut oil or another source of short-chain fats.

If we do (2) or (3), then the diet can be ketogenic even if it has a fair number of carbs.

I think so. Give it a try.