Nuclear equation of state is often described in the framework of energy density functional. However, the isovector channel in most functionals has been poorly constrained, mainly due to rather limited available experimental data to probe it. Only recently, the relativistic nuclear energy density functional with an effective point-coupling interaction was constrained by supplementing the ground-state properties of nuclei with the experimental data on dipole polarizability and isoscalar monopole resonance energy in Pb-208, resulting in DD-PCX parameterization. In this work, we pursue a complementary approach by introducing a family of 8 relativistic point-coupling functionals that reproduce the same nuclear ground-state properties, including binding energies and charge radii, but in addition have a constrained value of symmetry energy at saturation density in the range J = 29, 30, ..., 36 MeV. In the next step, this family of functionals is employed in studies of excitation properties such as dipole polarizability and magnetic dipole transitions, and the respective experimental data are used to validate the optimal choice of functional as well as to assess reliable values of the symmetry energy and slope of the symmetry energy at saturation.