"My ex-mother-in-law used to make this for holidays. I never did get her recipe. Years later I was at a potluck picnic when a friend showed up with this. The next day she gave me a copy of the recipe, and I have treasured it ever since."
Combine water and rice in a 3-quart saucepan. Bring to boil; simmer until water is absorbed and rice is tender, about 15 minutes. Allow to cool.
Mix sugar and flour together in a bowl. Stir sugar mixture, pineapple juice, and beaten eggs together in a saucepan; cook and stir over medium-low heat until the mixture has the consistency of pudding, about 5 minutes. Allow to cool.
Mix rice, pudding, pineapple, whipped topping, and cherries together in a bowl. Refrigerate until chilled, about 1 hour.