I do it by standing around in the 1-1 farm. I kill all the enemies then wait for the chickens to pop them out. It takes a long time. I've heard you might be able to get them from action replay but I don't have one.

Edit - accidentally said 1-2 farm.

1.) Stay on the farm in chapter 1-1 and wait for chickens to lay them. If the eggs stop spawning just re-enter the area.

2.) Kill a snake, hope to get a golden egg from it. If it doesn't drop the egg you want, reload the checkpoint. The egg color is always random, so you can just retry.

Golden eggs have a chance of like 5-10% to spawn.