I found the best trick ever for hard boiled eggs. Vinegar! A nice big splash of vinegar in the water any your eggs will peel like a dream.
When I am making my deviled eggs I make sure that I place the eggs tightly in the pot with the bigger side up. This insures that the bottom will be flat and that the yolk has a better chance of being in the middle.
Place the eggs in the pot and cover with water.
Bring the eggs to a boil and then turn off heat. Let the eggs sit in the water for about 15 minutes
Take eggs out of water and let sit until the have completely cooled.