AirPort Utility 5.6.1 for Mavericks
resolves a problem as old as OS X 10.9 itself: a system file upon which AirPort Utility relies was updated in 10.9 and that update broke backwards compatibility with AirPort Utility v5.6.1. The file in question is Apple80211 in /System/Library/PrivateFrameworks/Apple80211.framework/Versions/A. Replacing this file with the older version allows AirPort Utility v5.6.1 to be run under 10.9, but only via Terminal (i.e., double-clicking it will not launch it, it will throw an error).
However, there is a way to get around this issue by importing the older library into AirPort Utility v5.6.1
Version 1.2: Release notes were unavailable when this listing was updated.
OS X 10.9 or later