According to Martin Berkhan, a very small amount is OK (see the comment section: Intermittent Fasting, Set-Point and Leptin | Intermittent fasting diet for fat loss, muscle gain and health).
Martin gave a somewhat arbitrary number of 50 cals max to ensure that people weren't going overboard. That would be about a tablespoon by volume of heavy cream or 1.5 of coconut milk. At least according to nutritiondata. I thought coconut milk was similar in calorie content to heavy cream, but I guess it's lower, or maybe depends on the brand:
Nutrition Facts and Analysis for Cream, fluid, heavy whipping
Nutrition Facts and Analysis for Nuts, coconut milk, canned (liquid expressed from grated meat and water)