Place screenshots on Desktop on Display 2
I could never find a way to set this with a machine preference.  I ended up just creating a folder on my second monitor name "ScreenShots" and setting the default location for screenshots to that folder.  They will then save to that desktop and into that folder.

Change the default location to new folder on external monitor:    

defaults write com.apple.screencapture location ~/Desktop/ScreenShots/


Restart the SystemUIServer to make it take affect:

killall SystemUIServer