Higurashi no naku koro ni, for some yandere action, I kinda liked "Sola" too and that had a yandere.
Higurashi no Naku Koro Ni and the sequels Studio Deen did not fuck up Higurashi no Naku Koro Ni Rei and Higurashi no Naku Koro Ni Kai do not have yandere characters. It has yangire characters.
Yandere is the whole "deep love" kind of personality where someone loves you to the point where they will kill for you and sacrifice everything for you. Where the girl gets jealous and overly protective if another woman even looks at you. It's what you see in franchises like Mirai Nikki, School Days, Death Note, Rozen Maiden, Bludgeoning Angel Dokuro-chan and Code Geass: Lelouch of the Rebellion. Coincidentially most yandere characters are found in romance anime or anime with some romantic elements, though there are some rare exceptions.
Yangire is what you get when someone is sane one moment but just seconds later they flip out, go ballistic, and start mudering everything in sight. There is no love involved but instead something along the lines of mental illness, psychological trauma, or something else that affects the mind and causes a cute and adorable girl to become a foaming-at-the-mouth psychopath. It's the kind of thing you see in Higurashi no Naku Koro Ni, Cubed, Cursed, Curious, Rozen Maiden, Code Geass: Lelouch of the Rebellion, Deadman Wonderland, Fullmetal Alchemist and Dai Mahou Touge.
Please never confuse the two ever again.
Shion Sonozaki is arguable a Yandere character, though the object of her affection does not actually appear in the series itself.
^ I did actually look that up before I posted my suggestion, but more importantly, I looked at the shows the guy had seen and picked the
most appropriate series that he'd likely enjoy. Whereas your shows more "perfectly" fit the yandere trope, they're also nothing like the shows he mentioned. That's being pedantic to the point of failing to answer the original request. Your suggestions of Dokuro-chan, Code Geass and Death note for a guy who wants more shows like School Days and Mirrai Nikki? Really, well just no, those are way too different in feeling.
The odds are exactly zero that the guy who saw Mirrai Nikki and School Days will watch Higurashi and throw his remote down in disgust going "OMG! This is Yan
gire,
I specifically ordered Yan
dere". The guy obviously wants
"girls going axe crazy" and I doubt the exact relationship dynamics is going to matter as much as the screen time and emphasis.