Well if you aren't gonna allow the game window to be resized then you could just have an image that you draw over everything. If you want to allow resizing then you could create the image of the "scope" everytime the window is resized. I'm not entirely sure if either of these are the best way though since I've never tried doing that, and it's about 4am here xD

Good luck, I hope my suggestions at least help you think of something.
Z-Man

You could try drawing the scope in white on a full-screen black image and then using a multiply blending mode to composite over your background image.  If you're working directly with arrays of pixels you could check out this recent thread http://www.java-gaming.org/topics/some-new-blendmodes-add-multiply-overlay-etc/24529/view.html, or if you're just using Java2D then have a look at http://filthyrichclients.org/ -> Examples -> Chapter 6 which has a lot of additional blend modes for use with Graphics2D.setComposite().  The straight array mode will be faster, but the FRC code might be easier.

You might also try (less sure about this one) drawing your scope on a full screen transparent image and then setting the composite to AlphaComposite.DestIn before drawing it on top of your background.

Oh yeah!  For some reason I was expecting the scope to be an image rather than just a plain circle, despite the fact the OP distinctly used the word "circle" 

Depending on the other drawing you're doing it might also be worth clipping the background rendering to the bounding rectangle of the Area / scope as well - seems pointless to draw things that are going to end up black.