Have you installed the scenery very recently, or are you just trying to have the ParkMe running on an existing installation ?
Since the installer has an automatic online update for files like the Couatl engine, you can try running the JFK installer again, and let it update the Couatl.exe file with the current version.
The Couatl executable is launched automatically by FSX, you shouldn't launch it yourself. You can check if the installer has correctly updated your EXE.XML to have it automatically launched, by checking the %APPDATA%\Microsoft\FSX\EXE.XML file, and see if Couatl.exe has been added to it.
When FSX starts, you should have seen a request to trust it. Have you seen such request ? Have you trusted it ? Because if you haven't, or you decided not to trust it by mistake, Windows will never alllow to launch it again.
You can "clear" the list of trusted programs by editing the %APPDATA%\Microsoft\FSX\FSX.CFG file, removing ALL the lines that contains a Couatl.exe reference (the whole line), then saving the file and launching FSX again, you should get such trust request.
Again, do this using the current version of Couatl (update it online by running the installer again) and, if you are not sure, just download the whole JFK installer now.