Add the eggs to a medium saucepan and cover them with enough water so that it's 1 inch above the eggs. Place the saucepan over medium-high heat and bring the water to a boil. Once the water boils, cover the pan, turn off the heat and allow the eggs to cook for 12 minutes. Remove the eggs from the water and carefully peel them.
Slice the eggs in half lengthwise. Set aside the whites and add the yolks to a medium bowl.
To the bowl with the yolks, add the avocado, mayonnaise, mustard and sweet relish. Mash together the mixture with a fork then taste and season it with salt and pepper.
Transfer the mixture to a piping bag fitted with a star tip (optional) or sealable plastic bag. Pipe the mixture into the egg whites then garnish each deviled egg with three pieces of diced red pepper. Serve immediately or refrigerate, covered, until ready to serve.