Hello,
This is Melissa from the library. Did you email me a little bit ago? If so, I've been trying to answer your question, but it's been busy at the reference desk today.
I think we need to search something other than ERIC - something specific to libraries. There are two databases that might be helpful Library Literature and LISTA (Library Information Science & Technology Abstracts). I have links to both of them on a library science web guide at
http://libguides.unomaha.edu/libraryscience
Just click on the link title "Databases". Visually, the databases look similar but they cover many different journals so sometimes you need to search both.
I did a quick search in Library Literature on school libraries and academic achievement and found 23 peer reviewed articles between 2008-2013.
Also, I know of a researcher in Kansas who just linked school library staffing levels to AYP. Her article can be found at
http://www.ala.org/aasl/sites/ala.org.aasl/files/content/aaslpubsandjournals/slr/vol15/SLR_StaffingLevelsandStudentAchievement_V15.pdf
If this doesn't work, let me know and we'll try some other terms.
Melissa