Make deep cut in pointed end of each persimmon. Scoop out pulp into processor and puree until smooth. Measure 2/3 cup puree.
Combine milk, rice, honey, sugar, orange peel, and salt in medium saucepan. Bring to simmer, stirring until sugar dissolves. Reduce heat to low and cook, uncovered, until pudding is very thick, stirring frequently, about 40 minutes.
Add cranberries and cook until softened, stirring frequently, about 5 minutes. Remove from heat and stir in 2/3 cup persimmon puree. Serve pudding warm or at room temperature.
DO AHEAD: Can be made 2 days ahead. Cover and chill. Bring to room temperature before serving.