Place a sheet of parchment or wax paper on a baking sheet. Print out the rings template--see the note below for the template. Choose the size of the rings you want to make and cut the paper to only use that ring size. Slide the template underneath the parchment paper. (I used the 2 1/2-inch template for the rings on the cupcakes shown in the photos.)
Add the semi-sweet chocolate and black gel food coloring to a microwave-safe bowl. It will take a lot of black gel coloring, so add several drops and then add more until the desired shade is achieved. Melt the semi-sweet chocolate for 30 seconds. Stir. Melt for 30 more seconds. Stir until all the chips are melted.
Gather 1 sandwich bag, the round piping tip, and the tip coupler. Insert the coupler into the bag corner, snip off the corner of the bag, and then attach the piping tip and screw. (See the notes below for a link to see how to put together a coupler and piping bag.) You can also omit the coupler and place the tip into the bag. Cut the bag hole small enough that only half of the piping tip can fit through the bag corner. The coupler is not necessary but might provide more control for drawing circles.
Spoon the melted chocolate into the piping bag. Carefully "draw" chocolate over the end rings on the template. Slide the parchment paper over the template so you can make several rings. Each cupcake will take 1 black Olympics ring. When drawing a ring, the overlap where you start and stop will be a little thicker than the rest of the ring. When the black circles are all "drawn," place the cookie sheet into the refrigerator for 3-5 minutes to let them harden.
Wash the tip and coupler. Then melt 1/2 cup of white chocolate and add blue gel coloring. Repeat the process to make blue rings. Refrigerate them to harden the chocolate. Continue this process until all 5 ring colors are made and chilled.
Place 3 Olympic rings side-by-side into a frosted cupcake in the following order: blue, black, and red. Stick the thicker part of the ring where the chocolate overlapped into the frosting so it doesn't show. Place a yellow Olympic ring in front of the blue and black rings. Then place the green ring in front of the black and red rings. (Refer to the photos to see the rings.) This placement will give the appearance of overlapping rings.