Solar-powered and power grid connected green cellular networks are becoming attractive due to low carbon footprint and cost-effectiveness in providing uninterrupted service. In this paper, we analyze the performance of such dualpowered multi-cell network in presence of skewed traffic load across the different base stations (BSs). Cell coverage is decided at the network design stage based on long-term average traffic intensity across the various regions of a multi-cell coverage area. In presence of dynamically-changing skewness of traffic loads across different cells, we propose to adjust the cell coverage to accommodate the traffic and energy availability imbalance in the cells, while the demand for residual energy deficiency for serving the customers is fulfilled through the power grid connectivity. Network service provider's cost with the proposed coverage adjustment based strategy is compared with that of the conventional approach where the individual BSs do not undergo any cell coverage adjustment and seek to provide the maximum network performance. Our analysis and simulation-based performance results demonstrate, that the network performance as well as monetary gains of the service provider are significantly higher with our proposed strategy. For example, at a moderate (30%) traffic skewness, the proposed strategy offers about 4% gain in operator's annual profit, while serving about 8% more users on average at the peak hour. At a very high (80%) skewness, these numbers are respectively about 50% and 39%.