Is there any county-level (or similar) data on religious affiliation and church attendance in the United States from 1940s-1960s?
Here's the FAQ answer to what is available from the U.S. Census Bureau: https://ask.census.gov/prweb/PRServletCustom/YACFBFye-rFIz_FoGtyvDRUGg1Uzu5Mn*/!STANDARD?pyActivity=pyMobileSnapStart&ArticleID=KCP-5050
It suggests that data may exist for the period just before the date range you were hoping for. Perhaps that was what you were trying to extend? Here's the Pew Foundation's history of the debate surrounding the question of the propriety of the government doing such a survey.
The National Council of Churches has been doing surveys at the county level, but only did one in the time-frame your request. See links at http://www.usreligioncensus.org/ and http://www.thearda.com/Archive/Files/Descriptions/CMS52CNT.asp