While there is no one "magic" juice that will make you poop a lot, cranberry juice is a great option, but other juices can also help, including prune juice, apple juice, and pear juice. When opting for juices, choose all-natural products without added sugars or high fructose corn syrup, as these added sugars can actually contribute to constipation.
It is also good to dilute the juice with some water to cut down on the sugar content. Be sure to drink plenty of fluids when taking a fiber supplement because it can also cause constipation if you don't drink enough fluid.