Coconut oil is the latest wonder food in general, people are saying it's the be all and end all for humans as well. With basically negligible research. It is a saturated fat, so we've now come full circle with margarine now being the demon seed and a saturated fat the guy on the white horse.
So... my approach would be that it's a pure fat source, and a saturated fat source at that. Conures do need a bit more fat that some parrots, but if they are eating seeds and/or nuts and/or already have some fat supplement in their diets or a high-fat pellet, I'd be careful about the overall balance of fat in the diet. In suitable quantities it probably will do no harm (although I'm pretty sure there is no research on the effects of coconut oil on pet parrots) and might possibly do some good. Or not.
My motto is "keep an open mind, but not so open my brain falls out."