A four-component (4c) relativistic state specific multireference coupled cluster (4c-SSMRCC) method has been developed and applied to compute the ground state spectroscopic constants of Ag2, Cu2, Au2, and I2. The reference functions used in these calculations are obtained using computationally inexpensive improved virtual orbital-complete active space configuration interaction scheme. Rigorous size-extensivity and insensitivity towards the intruder state problem make our method an interesting choice for the calculation of the dissociation energy surface. To the best of our knowledge, this study is the first implementation of the SSMRCC within the relativistic framework. The overall agreement of our results, employing the smallest model space, with both theoretical and experimental reference values indicates that the 4c-SSMRCC method can be fruitfully used to describe electronic structures and associated properties of systems containing heavy elements. We observe a relativistic bond stabilization for the coinage metal dimers while the I-I bond is weakened by the relativistic effects.