Line a baking sheet with wax paper and set it aside. Sprinkle some confectioners sugar on a plate so you can dust your hands before you roll each ball of peanut butter later.
For the peanut butter balls, add your peanut butter, butter, vanilla and salt to a medium mixing bowl or the bowl of a stand mixer. Beat with a mixer until creamy. Gradually add your 1 1/2 cups of confectioners sugar, beating after each addition until blended. Your dough should be crumbly.
Using a small scoop if you have one, scoop about a teaspoon of dough. Dip your palms onto the plate of confectioners sugar and then roll the dough into a ball. Set the ball on your wax-paper lined baking pan. Continue scooping and rolling, dusting your hands with confectioners sugar each time so the dough won't be sticky. Insert a toothpick into each ball (until you reach the center of the ball) and then freeze the peanut butter balls on your baking sheet for an hour.
To prepare for dipping, have 5 or 6 paper dinner plates ready with a roll of wax paper. Just before you take the peanut butter balls out of the freezer, melt your chocolate chips and coconut oil in the microwave (use a microwave-save bowl). I heated mine on high for a minute, stirred, then heated it for 15 seconds, stirred, then heated it for another 15 seconds. Stir until the chocolate mixture is melted and smooth.
Take five peanut butter balls out of the freezer at a time and set them on a wax-paper lined plate. Using the toothpick as a handle, dip each peanut butter ball in the chocolate, leaving a circle of peanut butter exposed at the top. Dip once, lift it out, then dip again. Lift out the buckeye and let the chocolate drip off the bottom into your bowl. Set the buckeye on your wax-paper lined plate to dry. When you have dipped five buckeyes, pull out the toothpicks (if needed, you can gently press the buckeye with a toothpick held horizontally in one hand while you pull out the other toothpick with your other hand.) Using your fingertip, smooth over the toothpick hole until it's closed. Refrigerate your plate of buckeyes and grab another plate and five more peanut butter balls from the freezer. Continue dipping.
As soon as your chocolate starts to seize up (solidify) heat it in the microwave a bit until it's melted again, giving it a stir. Continue dipping the rest of your buckeyes in small batches, refrigerating them after dipping.
The buckeyes are ready when the chocolate is set. Store them in the refrigerator or freezer. If you need them for a party, freeze them, and when you are ready to serve them, set your platter of buckeyes on a tray of ice to keep the the chocolate from melting.
If using natural peanut butter, stir it if you just bought it and refrigerate the jar until it's chilled before using the peanut butter in this recipe. If you use semi-sweet chips, you might want to reduce the sugar by 1/4 cup, and if you use milk chocolate, you might want to reduce the sugar by 1/2 cup. You will have leftover melted chocolate (you need a good amount to be able to dunk the peanut butter balls.) You can refrigerate the leftover chocolate and heat it in the microwave to use for dipping fruit.