To the best of my knowledge, 1975 was the first tax year that the IRS Statistics of Income Division created a data file from returns.
SOI has a few studies listed here (http://www.irs.gov/taxstats/charitablestats/article/0,,id=97176,00.html) that date to the mid-70’s.
Of particular interest, the methodology for "Nonprofit Organizations, 1975 - 1978" (http://www.irs.gov/pub/irs-soi/75-78npo.pdf) states that a sample of 51,000 returns was created for the 1975 analysis (p.32 of the pdf) -- far larger than the samples created in the past decade.
At the time of this writing (March 2010), we are in the process of making additional inquiries with the IRS to see if the 1975 sample can be found.
When the National Center for Charitable Statistics moved to the Urban Institute in 1996, we attempted to obtain every possible IRS data file. Our contacts with the IRS resulted in us obtaining the files dating back to 1982. I feel confident that we would have received copies of any earlier data had our contacts there -- who I believe were quite knowledgeable -- been aware of them.
It was only in the 1960s that the IRS began to computerize its records on exempt organizations. My sense is that their computer systems were very difficult to manage and creating a dataset was a vastly more expensive and arduous undertaking than it is today thanks to the availability now of Form 990s in electronic format (begun in 1998) and the replacement of inflexible and difficult-to-program mainframe computers over the past several years!
If there is any other older national data, the place to find it is in the section on nonprofit organizations in the Historical Statistics of the United States (Millenial Edition) -- but I'm not optimistic.
Researchers such as Gerald Gamm and Robert Putnam -- "The Growth of Voluntary Associations in America, 1840-1940," Journal of Interdisciplinary History 29 (Spring 1999), pp.511-57 -- have collected data from individual associations of nonprofits and municipal records for their historical research, but this is a challenging process.
-- Tom Pollak, NCCS Program Director (and Assistant Dir. in 1996 when NCCS moved to Urban)