Emotional Deaths are pretty easy to get if you actively TRY to get them.
Probably the hardest would be Embarassed, and that's as easy as Flirting badly after having a Bladder failure.
Anger has multiple boosting moodlets, such as Angry Decorations and Angry Spaghetti, and that's before taking into account the side effects of Mean socials.
Hysterical is probably the easiest.
It's the only emotional death I have to try NOT to get!
Incredibly happy Sims can be done in by even a single +1 Playful moodlet if you're not careful.
Good food, beautiful decorations, high Needs, and so on. Happy moodlets stack up easily, and even a single Playful moodlet can turn them Hysterical after that.