The Cookies by Design icing/frosting recipe is not available on the Internet. You can use a royal icing recipe. Good luck.

Cookie Tip:
The key to beautifully decorated cookies that keep is royal icing. Royal icing dries to a hard, glossy finish which makes it perfect for decorating custom cookies.

Royal Icing
2 tbsp (30 mL) meringue powder*
1/4 cup (60 mL) water
2 cups (500 mL) icing sugar
1 tsp (5 mL) flavoring (vanilla, orange, lemon, maple, etc)

*available at specialty baking and cooking stores

Put your icing sugar, meringue powder and flavoring into a mixing bowl. Start your mixer on low and add water a little at a time until your icing reaches the desired consistency. The icing should be smooth and shiny. It is best to keep your icing a little stiff to begin as you can thin the icing later when you need it to decorate.

You can equally adjust the ingredients to make more or less icing. Feel free to add more water or more icing sugar to reach a consistency that you can decorate with.

Easy Decorating
Decorating cookies with icing can seem like a difficult task, unless you keep these tips in mind:

Take small portions of your icing for tinting with food coloring or icing dyes. Keep the icing you are not working with covered with a damp cloth or paper towel so it does not dry out.

Your cookies must be cool before you can decorate them.

Use a piping bag to distribute your icing onto your cookies for best results. If you don’t have one, try a small, resealable freezer bag with a tiny piece snipped off of the corner. Squeeze icing out through the corner onto the cookie.

Royal icing can be refrigerated for up to one week. To use out of the fridge, bring to room temperature and re-beat (you may need to add a little bit of water).

To stop icing from dripping down the sides of a cookie, pipe the icing along the edge of the cookie and let it set for 2-3 minutes. After it has hardened slightly, fill in the rest of the icing with a small knife.
If you have multiple piping bags or freezer bags with icing, when they are not in use, wrap a wet paper towel around the tip to prevent the icing from hardening.

If you make a mistake while decorating, simply take a butter knife, wipe the icing error away, and try again!

Let your icing on your decorated cookies dry for at least 6 hours before moving or serving. This will prevent them from smudging.

If you want black or brown icing, add melted unsweetened chocolate.