To prepare salsa, combine first 8 ingredients in a bowl; cover and chill.
To prepare the quesadillas, place 1 tortilla in a medium nonstick skillet over medium heat, and top with 1/2 cup cheese. Sprinkle with 2 tablespoons onions; top with a tortilla. Cook 3 minutes, pressing down with a spatula until cheese melts. Turn carefully, and cook until thoroughly heated (about 1 minute). Repeat procedure with the remaining tortillas, cheese, and green onions. Cut each quesadilla into sixths; serve with pear salsa.