I haven't been able to find anything about monitoring an external URL other than potentially the HTTP monitor. I found an HTTPS monitor (really how the site is handled) but from the documentation it seems to be an internal monitor only that requires access to WMI.
Is there an easy way to setup a monitor to verify a website is up?
Have you tried the "Web Transaction Watcher"?
This is a free tool from SolarWinds...
That should be the link for the tool, but if not, just go over to the tools section and get it there.
I hope it helps.