sudo -u peter /Applications/Safari.app/Contents/MacOS/Safari &
The -u switch specifies which user to run the process under (you'd use the logged-in user's username). The ampersand at the end prevents gibberish from being displayed in the console window while the application is running. If you run the above, then open Activity Monitor (or use top), you'll see Safari running under two processes (as well as have two Safari icons in the dock).
[robg adds: This seems to work, though I'm not sure how things like preference files are handled when multiple copies of the app are in use.]

