The Bureau of Labor Statistics publishes quarterly data on employment and wages based on businesses' reports for the unemployment insurance program. They just released a breakout of the data focusing on nonprofit organizations. Using that data, here's the average annual wage from 2012 in each state for employees of non-profit organizations:
DC had the highest nonprofit wage, at $66,053 per year, while Wyoming had the lowest at $31,744. Here's a table showing each state's average non-profit wage and each overall wage: