Spin-rotation constants for H-2, HF, N-2, CO and F-2 are calculated at the coupled-cluster singles and doubles level augmented by a perturbative correction for triple excitations together with large uncontracted basis sets. Explicit values for the lowest rovibrational states of these diatomics are obtained by solving the rovibrational Schrodinger equation with the finite-element method. Good agreement between theory and experiment is obtained for H-2, HF and F-2, while for N-2 and CO a thorough comparison with experiment is hampered by inaccuracies in the experimental numbers and the calculated values should be considered more reliable.