This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / American Horror Story: Coven
Cordelia finding out that she's infertile. She's clearly devastated, and when not even Marie Laveau will help because of how Fiona disrespected her, she's completely broken.
Cora, the mother of the boy killed by racists, talking about her son going to the new desegregated school.
FrankenKyle returns to Misty. She gives him a bath, but he starts to have flashbacks about what his mother did to him. Misty tries to calm him down, but he keeps screaming and yelling, until finally he breaks her radio, at which point she calls him a monster.
Madison's monologue at the beginning of The Dead. She hates herself for being unable to feel anything after all the shit she has been through.
The climax in "Head"- Delphine (well, her head) being forced to watch video and music from the Civil Rights Movement. Delphine, the murderous, sadistic racist, is moved to tears.
Really the whole scene of Hank's massacre of Cornrow City. The soul music about freedom and Delphine's tears did not help.
Hank's motive for shooting up Cornrow City: to protect Cordelia from the Voodoo witches.
Hank shooting Queenie in the stomach. Queenie then proceeds to take a gun and pull an Ate His GunHeroic Sacrifice to kill Hank by proxy with her voodoo doll powers and save Marie Laveau from also getting shot and killed by him.
Mitigated: Queenie survives.
Some people don't find that that much mitigating.
Misty not surviving the test of the seven wonders, she's stuck in her own personal hell for the rest of eternity and her physical body turned into dust so she can never be brought back.
To elaborate, Misty is stuck in a middle school science class where she is tasked to dissect a frog. Rather than doing so, she revives the frog, only to be forced to dissect it anyways. After which, she revives it. And is forced to dissect it again, and again, and again, for all eternity.
Cordellia cradling Misty in her arms and begging her to come back is probably more heartbreaking, especially if you shipped Foxxay.
In the opening of the finale there's a moment where Queenie is seen trying to communicate with Nan.
Queenie failing to bring Zoe back from the dead. At this point you can see she no longer cares about being Supreme and is more concerned about saving her friend.
Kyle's mother reacting initially seems unmoved by her son's death. Then she says she found his stash in his room, and has been smoking it while sleeping there nights. Largely undone by the end of the episode, where it's revealed she's been molesting him.
Nan's world-weary response to being drowned in a bathtub by Fiona and Marie as a sacrifice to Papa Legba. As he comes to lead her away to her own version of Hell, she simply says, "Anywhere's better than here."