How can I allow a non-root user to use ports below 1024?
If you can't change your app to use a port above 1024 then the easiest way would be to take the port it is using and map it to a port above 1024.

You can do that using the firewall, ipfw is the tool for setting the firewall. You could also do it using 'nc' - sometimes known as ncat or netcat.

There is a question here that gives more details. The thread also mentions "AuthBind" which is an open source package to that allows just this - opening ports below 1024 without granting root privileges.