After some agonizing, I replied that I do know of one, Nature's Song, which can be purchased at www.BiblicalNaturalHistory.org - but I added that there's no traditional basis for the notion that it's a segulah to say it for forty days, and that classical Judaism says that repentance, prayer and charity remove the evil decree, not saying Perek Shirah.
The person challenged me, asking on what basis I can declare this? I replied that, speaking as someone who literally wrote the book on it, I know of that which I speak. And that before I wrote the book on it, pretty much nobody had ever even heard of Perek Shirah - which shows that it can't be such an important part of Judaism anyway.
Despite my best efforts to sabotage my own book sale, the person bought it anyway. But for those of us who want to engage in traditional, classical Judaism, this is the time of year to be giving charity, not reciting Perek Shirah or swinging chickens. And as far as I've seen, there's no better charity than the Ramat Bet Shemesh-based charity Lemaan Achai.
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So, if you're looking for a good charity, I strongly recommend donating to Lemaan Achai at this link. And I hope that it serves as a role model for how all communal charity organizations should operate.