One good recipe for chewy coconut macaroons is the bakery-style coconut macaroon recipe from Layers of Happiness. This recipe calls for just six ingredients and takes approximately 30 minutes to make.
To make bakery-style coconut macaroons, use an electric mixer to beat four large egg whites and 1/2 teaspoon of almond extract in a large bowl until the mixture is very foamy. Add one 14-ounce bag of sweetened, shredded coconut, 1/2 cup of sugar, one 7-ounce tube of almond paste and one pinch of sea salt. Use a rubber spatula to mix these ingredients by hand until they are well blended.
Line a large baking sheet with parchment paper, and place balls of the macaroon dough onto the sheet. Keep the dough balls small and adequately spaced for bakery-like results. You can use your fingers to shape the dough. Keep a cup or bowl full of water handy for rinsing off sticky fingers between shaping each scoop.
Bake the cookies for 25 to 30 minutes in an oven that has been preheated to 325 degrees Fahrenheit. The cookies are done when they have set and turned golden brown. Allow the macaroons to cool for approximately 10 minutes before serving or transferring them to an airtight container.