In this study, we develop and implement a specialized coupled-cluster (CC) approach tailored for accurately describing atoms and molecules in strong magnetic fields. Using the open-source Ghent Quantum Chemistry Package (GQCP) in conjunction with the Python-based Simulations of Chemistry Framework (PySCF), we calculate potential energy curves, permanent and transient dipole moments, and vibrational spectra for the diatomic molecules H2, HeH+, and LiH under various magnetic field strengths, adopting a fully non-perturbative treatment. The main computational difficulties stem from the inclusion of the magnetic field in the Hamiltonian, in particular, from the presence of the angular momentum operator, which leads to a complication of the wave function and introduces a gauge-origin dependence. Addressing these challenges requires advanced modifications to existing routines, which we achieve by implementing gauge-including atomic orbitals (GIAOs) by using GQCP and the capabilities offered by PySCF. This approach enhances the accuracy and reliability of the CC theory, opening pathways for more comprehensive investigations in molecular quantum chemistry at strong magnetic fields.