The evolution of automated machine learning (AutoML) is gradually reengineering the design of deep learning architectures for various imaging tasks. AutoML effectively develops model architectures and tunes hyperparameters through neural architecture search (NAS). Deep learning model architecture design is generally considered a tedious and time-consuming task that requires mastery skills to develop robust and better-performing models for imaging tasks. Again, the model's hyperparameters must be well-tuned to ensure optimal performances, which can be tedious and time-consuming if the hyperparameters are manually selected; using existing hyperparameter optimization algorithms can be expensive regarding resources. This study addresses these challenges in developing an optimal convolutional neural network (CNN) for classifying Alzheimer's (AD). The study, therefore, adopted a NAS approach to generate a CNN model architecture using a customized search space comprising only CNN patterns implemented with a NAS framework. The search was done for ten (10) trials, yielding a CNN architecture with an accuracy of 95.85% and a loss of 0.22. Training the model with a 10-fold cross-validation approach using a 0.0009 learning rate for 150 epochs improved the model's performance. The model recorded 97.17% accuracy, 97.21% precision, 97.14% recall, and a 0.99 area under the curve (AUC) in classifying AD as one of AD, mild cognitive impairment (MCI), and normal control (NC). The model obtained 98.06%, 98.66%, and 98.62% accuracy on binary classes of AD/NC, AD/MCI, and NC/MCI, respectively. The model generally showed robustness and better performance than existing CNN architectures.