I've never done it myself, but I know that Processing (http://www.processing.org
) exports Mac (and PC and Linux) applications that you can run with a double click, and it doesn't rely on XCode or anything like that. It's all open source, so it should be fairly easy to figure out what's going on.
Taking a browse through the source, it appears that you'd most likely be interested in the function "public boolean exportApplication(int exportPlatform)" in the file at http://dev.processing.org/source/index.cgi/trunk/processing/app/src/processing/app/Sketch.java?view=markup
(search through it for that text). It looks like there's a skeleton application that it starts from, so you might have to track that down and download it. I'm not sure if any of what it does is Processing specific...
To me, though, it looks like the most likely thing you've missed is that you need to set your myApp.app directory to be executable ("chmod +x myApp.app") - even though the terminal won't let you execute it directly, Finder knows to call "open myApp.app" when you double click it (which will work in the terminal, but only if it's marked executable, otherwise you get a cryptic error). Try setting that, see if it does the trick.