Line a fine-mesh strainer with cheesecloth and place over a small bowl. Add the ricotta to the cheesecloth and let drain for 2 to 3 hours, refrigerated, to remove excess liquid.
In a medium bowl, whisk together the drained ricotta and confectioners' sugar until smooth; set aside.
In the bowl of a stand mixer, whip the heavy cream to medium-stiff peaks, about 5 minutes. Using a rubber spatula, gently fold the whipped cream into the ricotta mixture. Fold in the cookies and caramel sauce, creating a swirl effect; do not overmix. Chill in the refrigerator for at least 30 minutes.
Melt the chocolate according to the package directions. Dip both ends of each cannoli shell in the chocolate, shaking off the access. Dip one chocolate end of each cannoli shell in the toasted coconut. Place the dipped shells on a parchment-lined baking sheet. Let the chocolate set for at least 15 minutes before filling.
Just before serving, fill a pastry bag with the ricotta filling and cut off the tip (or fit with a large round piping tip). Pipe the filling from both ends of each cannoli shell to ensure it runs through the entire shell. Serve immediately.
Make the filling the same day as serving. If made a day ahead, the filling might be too loose.