Are there any journal articles in psychology that have promoted and discussed reproducible data analysis?
It's not a journal article, but it's a project, called Reproducibility Project.
They are re-doing psychological studies to estimate the reproducibility of a sample of studies. They try to stay as close as possible on the original study (they e-mail the author(s) for the exact stimuli etc.).
Here's the main site and here's the link to their spreadsheet.

This is a short article promoting the sharing of data in psychology. Another related study (by the same author) is also mentioned.