The ornamental design for an illuminating birdhouse, as shown and described.
FIG. 1 is a perspective view of an illuminating bird house showing my design;
FIG. 2 is another perspective view thereof; and,
FIG. 3 is an exploded perspective view of a second embodiment.
Short broken lines illustrate portions of the bird house or environment, and form no part of the claimed design. Long broken lines illustrate light rays illuminating openings and form no part of the claimed design.