As a person who does not live in Japan, who has never lived in Japan, and whose primary source of exposure to Japanese society comes from reading (mostly trashy) manga:How can you persuade someone not to do it (or change his mind about it)?
He couldn't.
I would argue that the point of this one-shot is that the protagonist didn't try to persuade his friend not to go through with it. For a split second it does seem that he might say something direct about seeing the book, but he ultimately takes the convenient out and just goes with the roundabout method of bringing the peaches.
I initially thought "that's very Japanese, to confront something so serious with such an indirect method because a direct confrontation could be unpleasant, embarrassing, etc.," but honestly I would expect this kind of reaction to be common in any society right now.
It's both tragic and touching. Society has conditioned this person to avoid an awkward conversation that might save a life, but he still tries to express his concern and (ineffectually) prevent the suicide by buying the peaches and delivering them under pretense. I actually did think the end was "cute" (for lack of a better word), but then of course I read the description / epilogue.