Instructions for setting this up with MythTV are here , but I found that I had to make a few changes to get things to work correctly. I modified one line of the shell script  as follows:

STATUS=$( xset -q | grep "Monitor is" | awk '{print $3}' )

To trigger the monitorpowerbutton.sh script, I placed the following into my /etc/lirc/lircrc file:

begin
 prog =  irexec
 button = TV_POWER
 repeat = 4
 config = /usr/local/bin/monitorpowerbutton.sh
end

Now my TV_POWER button toggles the power state of the monitor! 

Related posts:

1. Waiting for a HD HomeRun before starting the MythTV backend
2. Screen Scraping Amazon Album Art for MythTV