The best way to do this, is to create an automator service that's going to run a shell command, and then launch this shell command on keyboard key, which will be paired with a remote control button.
First open automator.
Go to file->new, and create a service
Make sure 'Services Receives' is set to 'no input'
Select run shell script. And enter the stript as follows: pmset displaysleepnow
Then go to file, save as a service. And save the file as 'Sleep Display'.
Go to system preferences, select Keyboard, go to the shortcuts tab. At the very bottom in general, you should now see 'Sleep Display.
You can now assign a keyboard shortcut to that, and then use the Flirc GUI to pair said keyboard shortcut with any remote control button. Make sure this shortcut is used no where else, or it will not work.