In a large bowl, beat the softened butter and peanut butter with an electric mixer on medium until smooth, scraping the bowl as needed; add the vanilla and mix to combine.
Add 1 cup of the powdered sugar and mix on low, then medium, until combined; continue adding the remaining powdered sugar one cup at a time until a thick, rollable dough forms (add up to 1/2 cup more if needed in 1/2 cup increments).
Line a cookie sheet with parchment paper. Scoop tablespoon-sized portions of dough (use a 1 tbsp scoop) and roll each into a smooth ball, placing them about 1 inch apart on the prepared sheet.
Insert a toothpick into the center of each peanut butter ball, then freeze the tray for at least 30 minutes until solid.
Place the chocolate chips and coconut oil in a microwave-safe bowl and heat at half power for 1 minute, stir, then continue heating in 30-second intervals, stirring between, until smooth (about 2 minutes total).
Use a large ice cream scoop or spoon to lift each frozen peanut butter ball and dip it into the melted chocolate, leaving a small circle of peanut butter visible at the top (about the size of a nickel); let excess chocolate drip back into the bowl and return to the parchment-lined sheet.
Freeze the dipped buckeyes for at least 15 minutes until the chocolate sets. Remove toothpicks and, if desired, dip a finger in a little water to smooth the toothpick hole on top.