Cerebellar ataxia (CA) is concerned with the incoordination of movement caused by cerebellar dysfunction. Movements of the eyes, speech, trunk, and limbs are affected. Conventional machine learning approaches utilizing centralised databases have been used to objectively diagnose and quantify the severity of CA. Although these approaches achieved high accuracy, large scale deployment will require large clinics and raises privacy concerns. In this study, we propose an image transformation-based approach to leverage the advantages of state-of-the-art deep learning with federated learning in diagnosing CA. We use motion capture sensors during the performance of a standard neurological balance test obtained from four geographically separated clinics. The recurrence plot, melspectrogram, and poincaré plot are three transformation techniques explored. Experimental results indicate that the recurrence plot yields the highest validation accuracy (86.69%) with MobileNetV2 model in diagnosing CA. The proposed scheme provides a practical solution with high diagnosis accuracy, removing the need for feature engineering and preserving data privacy for a large-scale deployment.