I'm seeking a list of how many prisoners got incarnated in each year in the US by private prisons compared to state-run facilities. Is such a list publically available?
There is tons of data at the US Bureau of Justice Statistcs - Corrections
But I think the best way is to get these data points from the two major private prison companies (CCA and GEO Group).
Luckily (for you), both are publicly traded - so you can download their annual reports and find all sorts of info about number of beds, and different types of housing.
For example, from the GEO Group 2012 annual report (PDF)
So then you just need to download a bunch of PDFs, and then copy/paste into a spreadsheet.
CCA annual reports (2008 - 2014) - http://www.cca.com/investors/financial-information/annual-reports
GEO Group annual reports (2001 to 2014) - http://www.snl.com/irweblinkx/FinancialDocs.aspx?iid=4144107
p.s. you can get more years of annual reports by contacting to the investor relations department