X-ray photon counting is a novel imaging technology gaining increasing academic and industrial interest due to its potential for high-resolution computed tomography (CT) and spectral CT. These photon-counting detector systems could have numerous benefits in medical imaging because they provide a substantial increase in the amount of available raw imaging information (e.g., multi-energy information). However, new algorithms are needed for using this information to increase the accuracy of diagnostic decisions. In this work, we focused on addressing technical challenges to consider when designing and building a laboratory benchtop for photon counting CT systems. We developed a photon counting cone-beam CT system containing a photon counting detector with a small detective area based on a translate-rotate geometry and a step-and-shoot acquisition mode. To control and synchronize the CT system components, we developed a desktop computer program with a user-friendly graphical user interface. Furthermore, we established a fully automated method for estimating some of the parameters that describe the geometry of the cone-beam CT system. This method is based on an iterative optimization technique in which the reconstructed image of a small sphere is evaluated to find the required geometrical parameters for better image reconstruction. Finally, we used images reconstructed from different scans to confirm the methodology used in the study.