Special equipment: a small (number 2) pastry tip
Cut the eggs in half lengthwise and remove the yolks to a medium bowl. Gently rinse the egg whites and pat dry with a clean cloth or paper towel. Lay the eggs flat on a paper-towel-lined baking sheet so they do not move around when filling.
Mash the yolks until smooth. Add 2 to 4 tablespoons of the mayonnaise and the mustard. Add the salt and pepper and mix until combined. Mix in the orange coloring to make the filling bright orange, like the color of a pumpkin.
Place the mixture into a piping bag for filling the eggs.
In a separate small bowl, mix the remaining 8 to 10 tablespoons mayonnaise and the black coloring until dark black. Place the mayonnaise in a small piping bag fitted with a small (number 2) tip.
Using a small knife, cut the green onions into 1/2-inch pieces for the stems of the jack-o-lanterns, and then place in a small bowl.
Pipe the orange filling into each egg half, making a round mound in the center to create the pumpkin. Pipe the black mayonnaise onto the filling: make two small triangles for the eyes and a zigzag line for the mouth. Place a piece of green onion at the top of the filling by the eyes to create the stem of the jack-o-lantern. Serve immediately or hold for up to 2 hours.
If making in advance, pipe the orange filling as the recipe instructs, but wait to pipe in the eyes and mouth until just before serving, as the color will bleed into the filling if left for too long.