I'd be wary of feeding too much coconut oil to any bird, it's very high in saturated fats. Our birds get only the oil in fresh coconut, and that, not very often. Having said that, my wife is SE Asian and she cooks with coconut cream a lot, so we are exposing ourselves to lots of nasty fats, if the nutritionists are correct. How true this is, is a matter for conjecture, SE Asians used few dairy products in cooking, yet have delicious, creamy curries, from coconut cream. As for beta carotene, I'd imagine there are many better sources, without checking possibly the orange fruits like pawpaw and mango, and of course carrots.