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There's currently no safe way to do this. You could try and make a copy of Ulysses and run that as a second "instance", but I really don't know what will happen to your projects, preferences etc. in the long run. Could get awfully corrupted, dunno.
Running two instances shouldn't be too complicated. It's a limit of Finder that allows only one instance at a time. Either you take fehnman's approach and just copy the app, or you use a command line command to start a second instance.
Preferences will probably not be corrupted, the ones of the version last closed will win over the other, so just don't change them. Also, you shouldn't open the same project twice. I can't give you a guarantee, but generally multiple instances shouldn't be problematic.