Toss the tomatoes, bell pepper, cilantro and 1/2 teaspoon salt in a medium bowl. Whisk the sour cream, mayonnaise, scallions, lime juice, chili powder and 1/2 teaspoon salt in a small bowl.
Assemble the salad: Sprinkle half of the cornbread in a glass bowl or trifle dish. Top with half each of the black-eyed peas, corn and the tomato-pepper mixture, then half each of the sour cream mixture and cheese. Repeat the layers with the remaining ingredients, ending with cheese. Cover with plastic wrap and refrigerate at least 2 hours or overnight.