Convolutional Neural Networks (CNNs) are being widely applied to the task of parking space classification, due to their high performance demonstrated in well-established state-of-the-art challenges. However, as deep learning models, CNNs encompass a large number of parameters, making the training and refinement process extensive, with loss functions and optimizers being two crucial training components that can help define the speed and quality of model training. Despite the wide use of these techniques in the literature, there is no consensus about the optimal combination for parking space classification, and a wide variety of different combinations have emerged. To address this concern, we propose a comparative study of loss function and optimizer combinations using a selected set of these functions and algorithms from the literature, with the aim of defining a possible optimal pair for this task. Using the PKlot dataset in our experiments, we show that the pair of Binary Cross Entropy (BCE) loss function and Stochastic Gradient Descent (SGD) optimizer has the best balance between accuracy and time required to train among the pairs created in this study, achieving an average accuracy of 98.2% and requiring approximately 4.6 epochs for fine-tuning.