Developing high-performing predictive models for large tabular data sets is a challenging task. The state-of-the-art methods are based on expert-developed model ensembles from different supervised learning methods. Recently, automated machine learning (AutoML) is emerging as a promising approach to automate predictive model development. Neural architecture search (NAS) is an AutoML approach that generates and evaluates multiple neural network architectures concurrently and improves the accuracy of the generated models iteratively. A key issue in NAS, particularly for large data sets, is the large computation time required to evaluate each generated architecture. While data-parallel training is a promising approach that can address this issue, its use within NAS is difficult. For different data sets, the data-parallel training settings such as the number of parallel processes, learning rate, and batch size need to be adapted to achieve high accuracy and reduction in training time. To that end, we have developed AgEBO-Tabular, an approach to combine aging evolution (AgE), a parallel NAS method that searches over neural architecture space, and an asynchronous Bayesian optimization method for tuning the hyperparameters of the data-parallel training simultaneously. We demonstrate the efficacy of the proposed method to generate high-performing neural network models for large tabular benchmark data sets. Furthermore, we demonstrate that the automatically discovered neural network models using our method outperform the state-of-the-art AutoML ensemble models in inference speed by two orders of magnitude while reaching similar accuracy values.