Position racks in the upper and lower thirds of the oven; preheat to 250 degrees F. Line 2 baking sheets with parchment paper.
Beat the egg whites, cream of tartar and salt in a large clean dry bowl with a mixer on medium speed until foamy. Increase the speed to medium high and beat until thick and opaque, about 1 more minute. Gradually add the confectioners' sugar, about 1/4 cup at a time, and beat until stiff shiny peaks form, about 5 more minutes.
Transfer the meringue to a pastry bag fitted with a large star tip. Pipe twenty-four 2 1/2-inch disks on the baking sheets, leaving space between each. Sprinkle with coarse sugar and/or silver nonpareils; bake at 250 degrees F until dry and crisp, 3 to 4 hours. Let cool completely on the baking sheets. Store in an airtight container in a dry place for up to 1 week.
For the filling, combine the white chocolate chips and coconut oil in a microwave-safe bowl; microwave, stirring every 30 seconds, until melted. Sandwich some white chocolate mixture and a lollipop stick between 2 cookies; repeat to make 12 lollipops. Let set.