Does anyone know of a good way to obtain data on the number of publications per year on a given subject? Scholar has an option to sort search results by date, but there does not seem to be an automated way of generating a report. In the worst case I will write a script that extracts the data I need, but perhaps someone knows of another system that offers such a facility? Thank you.
ISI Journal Citation Reports
ISI Journal citation reports might give you some useful information (your university may have a subscription). It allows you to browse citation reports by subject category (i.e., discipline). It includes things like impact factor, total counted citations, total articles in the focal year.
You can then click "view journal summary list" which will give you an overview.
For example, here is sample output for psychology in the 2013 JCR:
Of course, this only includes articles in journals indexed by ISI.
Publish or Perish Software
More generally, you might want to check out Publish or Perish. It is free software for Windows and OSX that provides a way of searching Google Scholar particularly suited to bibliometric analysis.
I don't know of a solution for arbitrary field and subject; I suspect none exists at present. But in mathematics, you could at least easily check how many publications there are each year in a given AMS subject classification.
For instance, this search result shows that 23 papers were published on Enumeration in graph theory in 2005. Note: you may need a subscription to access that link.