Replicating the remarkable adhesive properties of mussels in synthetic polymers continues to be of great interest for applications including self-healing materials, biomedical glues, and commercial underwater adhesives. Poly[(3,4-dihydroxystyrene)-co-styrene] (poly(catechol-styrene)) is a particularly promising material as it has been experimentally determined to outperform many synthetic adhesives, as well as the mussel system from which it is derived. Here, we develop catechol content specific coarse-grained (CG) models using an energy renormalization approach which captures the short time scale dynamics, self-diffusion, and segmental relaxation time at temperatures ranging from the glassy to Arrhenius regime. We compare the mechanical response of the CG and all-atomistic representations in order to demonstrate the predictive capability of the model into the nonequilibrium glassy regime. Our work makes detailed investigations into the mechanics of poly(catechol-styrene) possible and could help elucidate poorly understood trade-offs between surface wetting and polymer cohesion in mussel-inspired adhesives.