In a stand mixer fitted with a paddle attachment, beat the cream cheese until smooth and fluffy. Beat in the mint extract, then add 3 cups confectioners' sugar and mix until you have a fairly stiff mixture that holds together when you pinch it (you may need to add up to 1/2 cup more sugar, though 3 cups has always been enough for me).
Roll the mixture into small balls (the smaller, the cuter, but you might get bored and impatient, as I normally do!), then flatten each one slightly with the tip of your finger.
Melt the chocolate and coconut oil in a microwave or a double boiler and mix until smooth.
Use a fork or spoon to dip each Junior Mint into the chocolate mixture, then place each one on a parchment- or wax paper-lined baking sheet. Place in the refrigerator or freezer until the chocolate hardens, then serve.