Judging by the HTML source of the URL you gave, the authors are trying relatively hard to discourage the kind of thing you're trying to do. Maybe they feel that the API will change over time, or maybe they have legal reasons for it, who knows.
Anyway, perhaps the best approach (if you haven't already tried) would be to contact the site administrators and find out more about their policy for making the service available to other networked applications. Maybe they have a separate IP-based API that can be used, or maybe they would be willing to reconfigure their server to accept the GET request method and make your life easier.
Of course, it is possible to write a TCP/IP-based routine that will fake an HTTP POST to the server and get your results, but I haven't run across
one for LabVIEW.
Regards,
John Lum
National Instruments