Are you talking about coconut MILK or coconut water?
"Coconut milk" is made using the pulp of the coconut and is VERY high in saturated fat. I would not recommend "coconut milk" for a parrot. There are very few benefits for humans or pets to drink coconut milk. See nutritional information here:
http://nutritiondata.self.com/facts/nut ... cts/3113/2As for "coconut water" it has virtually ZERO fat, is low in cholesterol, and has good sources of electrolytes, potassium, manganese, riboflavin, calcium, and fiber. It is VERY good for human consumption, however, it has sodium and sugar, so it is probably not great for parrots long term, but I don't think it would be bad as a treat supplemented to their diet every once in a while. Nutritional information on coconut water can be found here:
http://nutritiondata.self.com/facts/nut ... cts/3115/2I would assume that the OP and other posters were talking about "coconut water", but I wanted to clarify the difference between the two, as they are very different and not interchangeable.
I buy young coconuts and drink the water from them all the time. It is very refreshing and is a lot like gatorade, in that it has a great source of electrolytes, and is better for you since it is much lower in sugar.
Something to be careful of is "coconut juice" or water with added sugar. Coconut water is often sold in cans with added sugar or high fructose corn syrup.
My favorite pre-packaged 100% pure coconut water is Vita Coco:
http://vitacoco.com/