1.
sprite.setColor(sf::Color(255, 255, 255, n));
2.
sf::Image image;
image.create(width, height, sf::Color::Red);
sf::Texture texture;
texture.loadFromImage(image);
sf::Sprite sprite(texture);
I don't remember if we still support texture-less sprites, you can try it:
sf::Sprite sprite;
sprite.setTextureRect(sf::IntRect(0, 0, width, height));
sprite.setColor(sf::Color::Red);
But what's wrong with sf::RectangleShape?