Solar-enabled systems are becoming popular for provisioning pollution-free and cost-effective energy solution. Dimensioning of a solar-enabled system requires estimation of appropriate size of photovoltaic (PV) panel as well as storage capacity while satisfying a given energy outage constraint. Dimensioning has strong impact on the user's quality of experience and network operator's interest in terms of energy outage and revenue. In this paper, dimensioning problem of solar-enabled communication nodes is analyzed in order to reduce the computation overhead, where stand-alone solar-enabled base station (SS-BS) is considered as a case study. For this purpose, hourly solar data of last 10 years has been taken into consideration for analysis. First, the power consumption model of BS is revised to save energy and increase revenue. Using the hourly solar data and power consumption profile, the lower bounds on panel size and storage capacity are obtained using the Gaussian mixture model, which provides a reduced search space for cost-optimal system dimensioning. Then, the cost function and energy outage probability are modeled as functions of panel size and number of battery units using curve fitting technique. The cost function is proven to be quasiconvex, whereas energy outage probability is proven to be convex function of panel size and number of battery units. These properties transform the cost-optimal dimensioning problem into a convex optimization framework, which ensures a global optimal solution. Finally, a Computationally-efficient Energy outage aware Cost-optimal Dimensioning Algorithm (CECoDA) is proposed to estimate the system dimension without requiring exhaustive search. The proposed framework is tested and validated on solar data of several cities; for illustration purpose, four cities, New Delhi, Itanagar, Las Vegas, and Kansas, located at diverse geographical regions, are considered. It is demonstrated that, the presented optimization framework determines the system dimension accurately, while reducing the computational overhead up to 94 percent and the associated energy requirement for computation with respect to the exhaustive search method used in the existing approaches. The proposed framework CECoDA takes advantage of the location-dependent unique solar profile, thereby achieving cost-efficient solar-enabled system design in significantly less time.