I don't know that I can tell you exactly how to do this, but there are at least two issues here.
First you must set the DISPLAY variable to the display the browser is to use. For example
will display on the first display.
Secondly, (and this is where my knowledge is really shaky) is that the browser is going to have to authenticate to the X server. I have done something perhaps a little in similar in that I have
ip-up.local, which is running as
root, pop an xterm up on a display. Because of where this was called from, the DISPLAY variable is already set. I then have the script
su to the user that owns that display to pop up the xterm. I am not sure if that will be sufficient for you, but hopefully this is enough info to at least get you started.