Rare earth elements and yttrium (REYs) are critical elements and valuable commodities due to their limited availability and high demand in a wide range of applications and especially in high-technology products. The increased demand and geopolitical pressures motivate the search for alternative sources of REYs, and coal, coal waste, and coal ash are considered as new sources for these critical elements. This research evaluates the REY potential of coals from Indiana (USA). However, although coal data revealed REY potential, it suffered from sparse samples with complete REY measurements. Therefore, we explore the applicability of machine learning (ML) models and data augmentation techniques to demonstrate their applicability to evaluate REY potential in Indiana, and other areas in coal basins, using selected coal parameters (Al2O3, Fe2O3, C, Ash, S, P, Mo, Zn, and As contents) as covariates (indicators). Due to the relatively small sample size with complete REY data in the Indiana Coal Database, two data augmentation techniques (Random Over-Sampling Examples and Synthetic Minority Over-Sampling Technique) were used. Four machine learning algorithms (linear discriminate analysis, support vector machine, random forest, and artificial neural networks) were applied for modeling REY potential as a classification problem. The results show that application of Synthetic Minority Over-Sampling Technique prior to development of the support vector machine (SVM) models generated the best REY classification with an accuracy of 95%. The encouraging results based on Indiana coal data may suggest that a similar approach can be used for other coal basins for screening the locations with REY potential. Those locations then can be targeted for more detailed geochemical surveys to identify most promising areas and evaluate overall REY resources.