Let be an integer. We introduce the notions of -FP-gr-injective and -gr-flat modules. Then we investigate the properties of these modules by using the properties of special finitely presented graded modules and obtain some equivalent characterizations of -gr-coherent rings in terms of -FP-gr-injective and -gr-flat modules. Moreover, we prove that the pairs (gr-, gr-) and (gr-, gr-) are duality pairs over left -coherent rings, where gr- and gr- denote the subcategories of -FP-gr-injective left -modules and -gr-flat right -modules respectively. As applications, we obtain that any graded left (respectively, right) -module admits an -FP-gr-injective (respectively, -gr-flat) cover and preenvelope.