I looked in Fsdreamteam folder in FSX and opened up the couatl folder and found a couatl application icon and double clicked it, started FSX and the couatl is in the drop down menu and works.
Ok, so your problem is not that Couatl doesn't work, is that it doesn't start automatically with FSX.
First, be sure you %APPDATA%\EXE.XML doesn't contain any errors, if you are not sure how to check it, post it here (don't post the file, ZIP IT into a .ZIP file and Attach the .ZIP file ). Or, just remove it, and reinstall GSX, so the installer will create a new one automatically.
Also, be sure you start FSX directly, not using some kind of other launcher.