Interionic interactions in conducting nanopores determine how counterions may be packed in the pores subject to the applied voltage. In ideal metals, interactions are exponentially screened by metallic electrons. However, modern nanoporous electrodes are predominantly made of carbon materials. To what extent is this screening affected by a different mode of dielectric response in such materials? To answer this question we study Coulomb interaction of charges in cylindrical and slit pores that allow finite electric field penetration into the pore walls, as well as the Coulomb interaction in a nanogap between two thin walls of graphene modeled by a non-local dielectric function. In all cases studied the screening was found to be subtly different than in metallic nanopores, but still strong enough to support realization of the so called superionic state in such pores.