Make a deep cut in the pointed end of each persimmon. Scoop out pulp. Place pulp in a food processor. Puree until smooth. This should measure about 2/3 cup puree. Reserve.
Stir together milk, rice, honey sugar, orange peel and salt in a medium, heavy bottom saucepan, over medium heat. Bring to a simmer. Stir until sugar dissolves. Reduce heat to low. Cook, uncovered, until pudding is very thick, stirring frequently, about 40 minutes.
Remove from heat and stir in vanilla, cranberries and persimmon puree.
Serve pudding warm or at room temperature. May be made 2 days ahead and refrigerated. Bring to room temperature before serving.