There are a few options. As a general method, stencil buffers often come in very handy where certain drawing needs to be masked out, like the outline where the circles overlap in your example.
In this case, I think this can be done just as easily without a stencil buffer. You can use the depth buffer to eliminate the outline where the circles overlap. The idea is that you draw the interior of the circles into just the depth buffer (since we don't want to see the interior), and then draw the outline. This way, the part of the outline that overlaps with another circle will be eliminated by the depth test.
The only caveat is that you have to be careful about depth fighting. You can use a small offset to make sure that the outlines are in fact behind the interior, and get eliminated by the depth test. An alternative would be to use
Let's say you have two circles that are parallel to the xy-plane, with centers at (x1, y1, z) and (x2, y2, z). And you have these draw functions:
// Draw interior part of circle, shown in green in the schematic in the question.
drawInterior(x, y, z);
// Draw outline of circle, shown in red in the schematic in the question.
drawOutline(x, y, z);
The sequence of drawing then looks like this, with
delta being a small offset:
glColorMask(GL_FALSE, GL_FALSE, GL_FALSE, GL_FALSE);
drawInterior(x1, y1, z + delta);
drawInterior(x2, y2, z + delta);
glColorMask(GL_TRUE, GL_TRUE, GL_TRUE, GL_TRUE);
drawOutline(x1, y1, z);
drawOutline(x2, y2, z);