In a medium bowl, mix 2 packages black cherry Jell-O with 2 cups boiling water and 1 1⁄2 cups cold water. Arrange half of the peaches around the bottom of a 3-qt. ring mold or Bundt pan. Add 1 1⁄2 cups of the Jell-O mixture to cover the peaches. Cover surface with plastic wrap and chill until firm, about 1 hour. Meanwhile, refrigerate the remaining black cherry Jell-O, stirring occasionally, until syrupy, about 35 minutes. Add syrupy Jell-O to the mold once the first layer is firm. Cover with plastic wrap and refrigerate.
In another medium bowl, mix lime Jell-O with 1 cup boiling water and 1 cup cold water. Refrigerate until syrupy, about 35 minutes. With a handheld mixer, blend cream cheese into the lime Jell-O. Add cream cheese mixture to the mold once the first 2 layers of black cherry Jell-O are firm and smooth the top with a rubber spatula. Cover and refrigerate until firm, about 1 hour.
Meanwhile, mix the remaining packages of black cherry Jell-O with 2 cups boiling water and 1 1⁄2 cups cold water. Refrigerate until syrupy, about 35 minutes. When the layer of lime Jell-O is firm, add the remaining peaches to the mold and cover them with the remaining black cherry Jell-O. Cover and refrigerate until firm, at least 2 hours or overnight.
To serve, invert mold onto a plate. Soak a towel in warm water and rub it over the top of the mold. Gently lift the mold off the gelatin. Slice gelatin and serve.