Aims: Monitoring sleep states in Intensive Care Unit (ICU) is important for assessing the health status and neurodevelopmental maturation of newborns, especially those born preterm, i.e., before 37 weeks of gestation. However, traditional manual monitoring based on behavioral observations is subjective and time-consuming, making it challenging to implement in ICU. This study proposes an automated approach for estimating Quiet Sleep (QS), a crucial sleep stage for preterm neonates' growth and development, using Machine Learning Algorithms (MLAs). The proposed approach utilizes cardiorespiratory variability and body motion information to estimate QS. Methods: The proposed approach was evaluated on manually annotated recordings from 15 newborns. Each newborn was recorded for eight hours during their first week of life, and preterm newborns were recorded again at 37 weeks postmenstrual age (PMA). A total of 77 cardiorespiratory features, derived from RR and respiratory intervals, were extracted from both time and nonlinear domains in each recording, including PMA as a feature. After feature selection, leave-one-out (LOO) cross-validation method was used to compare MLAs and identify the best hyper-parameters. To correct false estimates, predicted QS states of the selected model were combined with body non-motion intervals, which is a typical characteristic of QS. Results: Only 5 cardiorespiratory features combined with PMA were selected. The Random Forest algorithm demonstrated the highest performance during LOO. When combined with body motion, it achieved an average balanced accuracy of 78% and a Cohen's kappa of 0.51 across all recordings. For neonates with a PMA greater than 33 weeks, these values increased to 82% and 0.6, respectively. These results outperform our previous findings and current state-of-the-art cardiorespiratory-based approaches. Conclusion: This study demonstrates that MLAs can accurately estimate QS of neonates using non-invasive signals. The identification of a compact set of only 6 features for predictions also increases the interpretability of the approach.