Crying is one of the means of communication for a newborn. Newborn cry signals convey precious information about the newborn’s health condition and their emotions. In this study, cry signals of healthy and pathologic newborns were analyzed for the purpose of developing an automatic, non-invasive, and comprehensive Newborn Cry Diagnostic System (NCDS) that identifies pathologic newborns from healthy infants. For this purpose, Mel-frequency Cepstral Coefficients (MFCC) and Gammatone Frequency Cepstral Coefficients (GFCC) were extracted as features. These feature sets were also combined and fused through Canonical Correlation Analysis (CCA), which provides a novel manipulation of the features that have not yet been explored in the literature on NCDS designs, to the best of our knowledge. All the mentioned feature sets were fed to the Support Vector Machine (SVM) and Long Short-term Memory (LSTM). Furthermore, two Hyperparameter optimization methods, Bayesian and grid search, were examined to enhance the system’s performance. The performance of our proposed NCDS was evaluated with two different datasets of inspiratory and expiratory cries. The CCA fusion feature set using the LSTM classifier accomplished the best F-score in the study, with 99.86% for the inspiratory cry dataset. The best F-score regarding the expiratory cry dataset, 99.44%, belonged to the GFCC feature set employing the LSTM classifier. These experiments suggest the high potential and value of using the newborn cry signals in the detection of pathologies. The framework proposed in this study can be implemented as an early diagnostic tool for clinical studies and help in the identification of pathologic newborns.