The deployment of Self-Organizing Networks (SONs) based architectures has emerged as one of the key points in the 3GPP LTE-Advanced Standard, which aims to embed auto-management skills into the next generation mobile networks. However, the high traffic demands and the increased number of nomadic users have led dense eNodeB coverage, thus challenging the SON management in terms of energy efficiency. Considering these crucial SON challenges, we propose a novel adaptive network coverage model for energy-efficient SONs using a special spatial optimization method. This novel method is based on the Voronoi diagram optimization to provide the minimum number of active eNodeBs for high energy saving. The proposed model mathematically analyzes all the operating eNodeBs deployed in a specific SON area in terms of the utilization, by identifying them by a two-parameter function. These are the spatial coordinates and the utilization of the eNodeB. This eNodeB-specific mathematical model leads to find the redundant eNodeBs with less utilization, deactivate them and rearrange the coverage area with the remaining active eNodeBs using the Voronoi specific optimization. This optimization is solved by a novel heuristic with the aid of a parameter called assignment factor, in order to maximize the utilization for the remaining active eNodeBs in the green SON architecture. This spatial optimization based algorithm aims to adaptively deploy energy-effective cell coverage. The thorough evaluation results prove the generic energy-efficiency of the proposed adaptive coverage algorithm while maintaining the ENodeB utilization above the satisfying QoS levels.