Our for-profit company, Lambda, uses Xero, a web-based accounting tool. They claim to serve non-profits as well: http://www.xero.com/us/not-for-profit/
I can’t speak to how good they are for non-profits, but many startups are using Xero these days.
Strongly agree that you would have a much, much higher impact by making this game available on the web. Straight-up Java is pretty much dead now. Consider even making a Facebook app, which would allow players to share the game with their friends for stronger distribution.