It takes several thousand years for the deep-ocean concentration of tracers to come to equilibrium with surface fluxes, making it computationally too expensive to perform the large number of marine biogeochemical model simulations to objectively calibrate uncertain parameters. We present an offline implicit tracer solver that requires the equivalent of only a few tens of model years as opposed to thousands of years to reach equilibrium. The solver uses a Newton-Krylov algorithm with a preconditioner based on a coarse-grained annually-averaged tracer- transport operator. Coarse-graining provides a general approach for developing preconditioners for models of increasing resolution. We implemented and tested the solver for the ocean component of the Community Earth System Model (CESM) with a nominal horizontal resolution of 1x1 and with 60 vertical levels. We demonstrate the use of the solver for simulating phosphate, dissolved organic matter and radiocarbon. For the radiocarbon simulation we find a substantial bias in the North Pacific that translates to water mass ages that are twice the observationally based estimate. This bias is substantially larger than published simulations obtained with coarser resolution models, suggesting that increasing model resolution does not automatically improve the fidelity of the deep ocean ventilation processes. The implicit offline model makes it feasible to use tracers such as natural radiocarbon to help constrain uncertain physical and biogeochemical parameterizations.