Other people may not think so, but I can't imagine mixing coconut oil with eggs. ICK. I like butter. Use ghee or clarified butter if you can because it doesn't burn.
The pan has to be HOT. Hot enough to sizzle the eggs when they hit the pan, not just warm enough to melt the butter. This is important. The underside of the egg liquid has to cook and solidify immediately. If the egg stays liquid for even a few seconds, then the melted butter underneath will float to the top. The eggs will touch the pan without a layer of fat and they WILL stick.
5'0" female, 43 years old. Started Primal October 31, 2011, at a skinny fat 111.5 lbs. Low weight: 99.5 lb on a fast. Gained to 110 on sugar cheat. Reset with 85P / 90C / 90F. Currently weaning off fat to 85P / 90C / 60F.
MY PRIMAL: I (try to) follow by-the-book primal as advocated by Mark Sisson, except for whey powder and a bit of cream. I advocate a two-month strict adjustment for newbies. But everybody is different and other need to tweak Primal to their own needs.