Line a fine-mesh strainer with cheesecloth. Put the chocolate in a heat-resistant bowl and set aside.
Combine the coffee, sugar and 1 3/4 cups water in a medium saucepan. Bring to a boil, then reduce the heat to low, and simmer for 4 minutes, stirring constantly. Strain over the chocolate and let sit for 2 minutes before whisking until the chocolate is melted. Let cool at room temperature, then refrigerate for at least 30 minutes or up to overnight.
With a whisk, whip the cream in a medium bowl until it holds soft peaks. Remove the chocolate mixture from the refrigerator and slowly pour into the cream; whisk until smooth.
Pour into 6 ice pop molds and freeze for at least 4 hours.