I would like to replace part of the sugar with another ingredient, and since applesauce is already replacing part of the oil, what do you suggest?

What sort of ingredient are you thinking of replacing it with? Quick breads need sugar for structure, unless you were aiming for a honey or agave based bread recipe, I wouldn't remove much of the sugar. You COULD use a mostly unsweetened jam or fruit spread as a replacement, making an apple-fruit-zucchini bread.