Combine the water and 1 cup of sugar in a medium saucepan. Warm over medium heat, stirring, just until the sugar dissolves. Don't let it boil hard.
Remove the pan from the heat and let the syrup cool until it's just warm, about 10 to 15 minutes. Hot syrup will make the cranberries split.
Put the cranberries in a bowl and pour the warm syrup over them. Stir so every berry is coated, then cover and refrigerate for about 8 hours or overnight.
Drain the cranberries, saving the syrup if you like. Spread them on a wire rack set over a sheet pan and let them dry for about 1 hour, until tacky but not wet.
Put the rolling sugar in a shallow dish. Roll the cranberries a handful at a time until they are well coated.
Spread the sugared cranberries on parchment and let them dry for about 1 hour, until the coating is set. Serve or refrigerate.