The government measure is probably pretty accurate.
I’m not aware of any private numbers.
If you find some, please let me know.
One, recently developed by economists Roberto Rigobon and Alberto Cavallo, is the MIT's Sloan School of Management Billion Prices Project (BPP) (http://bpp.mit.edu/ ).
They have slightly different inputs but, in general, are pretty comparable to the U.S. government's BLS indexes, especially over the longer periods, as most price inflation indexing schemes' input-related spikes are generally "self-correcting" over time.
Data for the USA is at http://bpp.mit.edu/usa/
Ref: NIA Backs Sarah Palin In Inflation Dispute - FR, post #6, 2010 November 17
Ref: Misconceptions about the CPI (FR Thread to Prove or Disprove CPI and Shadow Stats)(17page PDF file) - FR, posts #31, #40, 2011 April 15