In a large skillet cook chicken and chopped onion over medium heat until chicken is no longer pink, using a wooden spoon to break up chicken as it cooks. Drain off fat. Add coriander, cumin, and salt to chicken mixture in skillet; cook and stir for 1 to 2 minutes. Add tomatoes, potato, dried plums, and olives. Bring to boiling; reduce heat. Cover and simmer about 10 minutes or until potatoes are tender. Uncover; cook about 3 minutes more or until most of the liquid has evaporated.
Meanwhile, heat tostada shells according to package directions until crisp. Arrange shredded romaine on a serving platter. Spoon chicken mixture over romaine. Sprinkle cheese over all. Coarsely crush the tostada shells; sprinkle over salad. If desired, garnish with green onion and/or cilantro.