In large nonstick skillet heat oil over medium heat. Add onions, ginger, and garlic. Cook, about 5 to 6 minutes, stirring occasionally, until tender and translucent. Stir in cinnamon and allspice; cook about 15 to 20 seconds, until fragrant. Add cherries, pomegranate juice, and sugar.
Increase heat to medium-high. Bring onion-cherry mixture to boiling. Reduce heat to medium-low. Simmer, uncovered, about 30 minutes, stirring occasionally until onion-cherry mixture is thickened. Remove from heat. Stir in pomegranate seeds and salt. Refrigerate chutney, covered, up to 1 week. Makes 1-3/4 cups.