Accurate estimation of global solar radiation (GSR) is essential for solar energy system design, climate studies, and environmental modelling. In Nigeria, direct measurements of solar radiation remain limited due to sparse instrumentation and frequent data gaps, necessitating reliable empirical models. This study evaluates seven established cloud-cover based models and develops five new models (NDM1–NDM5) for improved prediction of GSR across Nigeria’s four major climatic zones: Sahel Savannah (Potiskum), Sudan Savannah (Yelwa), Guinea Savannah (Ibi), and Tropical Rainforest (Calabar). Long-term meteorological data spanning 32 years (1990–2021) were obtained from NiMet. Extraterrestrial radiation was computed using standard solar geometry, and model performance was assessed with ten statistical indicators, including MBE, MAE, RMSE, MPE, MARE, and the correlation coefficient (r). A Global Performance Indicator (GPI) was employed to rank model performance. Results show significant variation in the accuracy of the existing models across climatic zones. The newly developed models consistently outperformed the literature models, with NDM5 emerging as the best-performing model in three of the four climatic zones, exhibiting very low RMSE, minimal bias, and high correlation (r > 0.96). In the Tropical Rainforest zone, where cloud cover is persistently high, NDM4 showed superior stability compared to other models. Overall, the new models demonstrated improved sensitivity to seasonal cloud cover variability and reproduced measured GSR more accurately across all zones. The study concludes that cloud-cover based models can reliably estimate solar radiation in data-sparse regions and that the newly developed models offer a more generalized and climate-responsive framework for Nigeria.