Combine 1 cup water, rice and evaporated milk in a 2- to 3-quart round slow cooker.
In a small saucepan, cook sugar and milk over medium-high heat for 1 minute or until bubbles appear around edges and sugar has dissolved. Stir into slow cooker with salt. Cover and cook on LOW for 41/2 hours.
While rice is cooking, bring cherry juice to a boil and pour over cherries in a small bowl; let stand 10 minutes. Drain, reserving juice.
Stir cherries, 3 tbsp of the warm juice, the cinnamon and nutmeg into slow cooker; cover and cook on LOW for 20 minutes more.
Turn off slow cooker and allow pudding to cool, partially covered, for 30 minutes.