2D profiles of electron density and neutral temperature are inferred from multi-delay coherence imaging spectroscopy data of divertor plasmas using a non-linear inversion technique. The inference is based on imaging the spectral line-broadening of Balmer lines and can differentiate between the Doppler and Stark broadening components by measuring the fringe contrast at multiple interferometric delays simultaneously. The model has been applied to images generated from simulated density profiles to evaluate its performance. Typical mean absolute errors of 30% are achieved, which are consistent with Monte Carlo uncertainty propagation accounting for noise, uncertainties in the calibrations, and in the model inputs. The analysis has been tested on experimental data from the MAST-U Super-X divertor, where it infers typical electron densities of 2-3 1019 m-3 and neutral temperatures of 0-2 eV during beam-heated L-mode discharges. The results are shown to be in reasonable agreement with the other available diagnostics.