Divide the pudding between two bowls (each needs to be able to hold about a cup). Add red coloring to one bowl, to desired shade of red.
Place two tablespoons of the vanilla pudding in the bottom of each mold. Lightly tap until it's level. Repeat the process with the red colored pudding and alternate until you reach the top. Wipe the sides with a paper towel if they get too messy.
Place the sticks in the molds and freeze them for at least eight hours. You can release the pudding pops by quickly running the mold under warm water.
Remove these pops from the molds, wrap them individually in plastic and return them to the freezer while the next batch freezes if you're doing this for a larger group.