We present results of the design, implementation and testing of a Bayesian multi-diagnostic inference system which combines various divertor diagnostics to infer the 2D fields of electron temperature Te, density ne and deuterium neutral density n0 in the divertor. The system was tested using synthetic diagnostic measurements derived from SOLPS-ITER fluid code predictions of the MAST-U Super-X divertor which include appropriate added noise. Two SOLPS-ITER simulations in different states of detachment, taken from a scan of the nitrogen seeding rate, were used as test-cases. Taken across both test-cases, the median absolute fractional errors in the inferred electron temperature and density estimates were 10.3% and 10.1% respectively. Differences between the inferred fields and the test-cases were well explained by solution uncertainty estimates derived from posterior sampling. This work represents a step toward a larger goal of obtaining a quantitative, 2D description of the divertor plasma state directly from experimental data, which could be used to gain better understanding of divertor physics phenomena.