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Estimates of national immunization coverage are crucial for guiding policy and decision-making in national immunization programs and setting the global immunization agenda. WHO and UNICEF estimates of national immunization coverage (WUENIC) are produced annually for various vaccine-dose combinations and all WHO Member States using information from multiple data sources and a deterministic computational logic approach. This approach, however, is incapable of characterizing the uncertainties inherent in coverage measurement and estimation. It also provides no statistically principled way of exploiting and accounting for the interdependence in immunization coverage data collected for multiple vaccines, countries and time points. Here, we develop Bayesian hierarchical modeling approaches for producing accurate estimates of national immunization coverage and their associated uncertainties. We propose and explore two candidate models: a balanced data single likelihood (BDSL) model and an irregular data multiple likelihood (IDML) model, both of which differ in their handling of missing data and characterization of the uncertainties associated with the multiple input data sources. We provide a simulation study that demonstrates a high degree of accuracy of the estimates produced by the proposed models, and which also shows that the IDML model is the better model. We apply the methodology to produce coverage estimates for select vaccine-dose combinations for the period 2000-2019. A contributed R package {\tt imcover} implementing the No-U-Turn Sampler (NUTS) in the Stan programming language enhances the utility and reproducibility of the methodology., Comment: 31 pages (main), 4 figures