Place a medium saucepan over medium-high heat and allow it to heat up for a minute. Once the pan is hot, add 2 tablespoons of amaranth. Heat, stirring constantly and shaking the pan gently. After a few seconds the amaranth seeds should start to pop. Cook until most have popped, about 2 minutes. They'll start to burn before they all pop, so once the popping begins to slow down or you see some burned seeds, remove the pan from the heat and pour the amaranth into a bowl. Repeat with the remaining amaranth, popping 2 tablespoons at a time.
Preheat the oven to 300°F and line a couple of baking sheets with parchment paper.
Place the popped amaranth into a large mixing bowl with the oats, coconut, and peanuts, and stir until evenly mixed. In a small bowl or liquid measuring cup, stir together the peanut butter, maple syrup, oil, vanilla, and salt. Add the peanut butter mixture to the bowl with the oats and stir until evenly mixed.
Spread the mixture in even layers on the prepared baking sheets. Bake until lightly browned around the edges, about 30 minutes. Remove from the oven and allow to cool. Serve or store in an airtight container for later use.
If you find the amaranth burns at first, try popping just one tablespoon at a time.