Are you confident that the two-tone color scheme is accurate? For my own personal tastes I'd probably choose either solid silver or solid bronze...
What I am entirely confident about is that Cooper's pin is the smaller variant of the Soka Gakkai pin. The size and details perfectly match.
The two-tone color scheme is a little harder to verify. I too had previously assumed that Cooper's pin was one solid color. But I believe it is accurate.
First off, the two-tone color scheme is dependent entirely on the condition of each individual pin. Here is an image of the larger variant of the pin, being sold on eBay by the same seller as the smaller one, and its materials are described as exactly the same as the smaller variant (crane is bronze, petals are silver) and yet the pin looks much more like it's a single tone rather than two:
The bronze portion is described as "peeling a bit," which suggests that if Cooper's pin looks one-tone, it may simply be slightly weathered/damaged.
Second, the difference in color is easier to see in certain lighting conditions, and borderline indistinguishable in others. It may be that we only see Cooper's pin when it's photographed in direct lighting (as it is a TV show that undoubtedly used strong lighting, not to mention the warm color tones of the series that would minimize any hint of silver in the pin and make it appear warmer, likely gold/bronze-ish). Here is what my pin, ordered from that seller who posted the image that looks distinctly two-toned, looks like under direct indoor lighting (no flash):
Compare to the seller's photo:
Mine looks pretty much like solid bronze to me in that lighting. In other lighting conditions, its two-toned scheme is more noticeable.
And finally, here are some screenshots (in which I attempted to fix the white balance, to make judging colors more objective) that may verify the two-toned look, though it's still a bit hard to tell because the tiny pin never gets a close-up:
Click to see larger. To my eyes, at least, the crane center is darker and "yellower" than the lighter-colored petals surrounding it, suggesting that the two-toned pins this seller is carrying are screen-accurate.