How can I restart a IIS site by using appcmd commands?

You have a couple of options here:

To restart an individual app pool, try (Reference):

appcmd recycle apppool /apppool.name: string

OR

 appcmd stop apppool /apppool.name: Marketing 
 appcmd start apppool /apppool.name: Marketing 

To restart an individual website, try (Reference)

 appcmd stop site /site.name: contoso 
 appcmd start site /site.name: contoso

or you could restart the whole IIS server:

iisreset

I think this works on IIS 7.5 It definitely does on 7.0 and I've been informed by a colleague that it does on 8, so no reason to believe 7.5 won't

Hope this helps

Ok, I was able to get it working on IIS 7.5 by changing the following details in the @Fazer87's command:

Instead:

appcmd start site /site.name: contoso

Change to:

appcmd start site "my_real_site_name.com" (also note the double quotes)