Do you know if there exists a database for the type of data you are interested in? That would be the easiest way: browse the database until you find an interesting data set, and the paper will likely be referenced by the database entry (if it is a serious database).
Here is an analogy with my own field (structural biology): most (if not all) journals require that structural models of biological molecules be deposited in the PDB in order to publish the article describing the structure. Only the model used to be deposited, but nowadays researchers are also encouraged to deposit the data that led to the model. Therefore, if I am looking for the article describing a particular structure, it is often easier to look up the molecule in the PDB, possibly choose between different entries (one of they may have associated data, not only the model) and find the paper from there.