Abstract: As part of the data-driven paradigm and open science movement, the data paper is becoming a popular way for researchers to publish their research data, based on academic norms that cross knowledge domains. Data journals have also been created to host this new academic genre. The growing number of data papers and journals has made them an important large-scale data source for understanding how research data is published and reused in our research system. One barrier to this research agenda is a lack of knowledge as to how data journals and their publications are indexed in the scholarly databases used for quantitative analysis. To address this gap, this study examines how a list of 18 exclusively data journals (i.e., journals that primarily accept data papers) are indexed in four popular scholarly databases: the Web of Science, Scopus, Dimensions, and OpenAlex. We investigate how comprehensively these databases cover the selected data journals and, in particular, how they present the document type information of data papers. We find that the coverage of data papers, as well as their document type information, is highly inconsistent across databases, which creates major challenges for future efforts to study them quantitatively. As a result, we argue that efforts should be made by data journals and databases to improve the quality of metadata for this emerging genre.