The evolution of IoT based smart applications demand porting of artificial intelligence algorithms to the edge computing devices. CNNs form a large part of these AI algorithms. Systolic array based CNN acceleration is being widely advocated due its ability to allow scalable architectures. However, CNNs are inherently memory and compute intensive algorithms, and hence pose significant challenges to be implemented on the resource-constrained edge computing devices. Memory-constrained low-cost FPGA based devices form a substantial fraction of these edge computing devices. Thus, when porting to such edge-computing devices, the designer is left unguided as to how to select a suitable systolic array configuration that could fit in the available hardware resources. In this paper we propose Systimator, a design space exploration based methodology that provides a set of design points that can be mapped within the memory bounds of the target FPGA device. The methodology is based upon an analytical model that is formulated to estimate the required resources for systolic arrays, assuming multiple data reuse patterns. The methodology further provides the performance estimates for each of the candidate design points. We show that Systimator provides an in-depth analysis of resource-requirement of systolic array based CNNs. We provide our resource estimation results for porting of convolutional layers of TINY YOLO, a CNN based object detector, on a Xilinx ARTIX 7 FPGA.