Things that can help stave off a tantrum spiral:
A good mayor is very helpful when tempers are short, since angry dwarves arrange meetings with the mayor...one with high social skills can calm them down, it's believed that "consoler" is particularly important, though I'm not sure there's much ‼science‼ on which social skills are most important in mayoral meetings. Turn off the mayor's labors, so meethings happen promptly and dwarves get calmed down faster.
Job satisfaction - Take an unhappy dwarf. Look at their preferences. Order them to make or use something that they like, by making them the only one with the corresponding labor turned on and queuing a job, or a few jobs. I'm fairly certain will give them the "satisfied at work lately" happy thought (no testing on my part to confirm that theory, but I've seen anecdotal evidence, e.g. miners that like picks having that thought).
Legendary dining - Make sure you have a dining hall set up, with enough space for everyone that wants to eat. It helps if the chairs and tables are highly valuable, as dwarves will often admire them, but if you can't get masterworks, just a large dining facility will work wonders...dwarves see any large dining room as "legendary", and get the "dined in a legendary dining room recently" happy thought when they eat there.
No rations - Military dwarves that carry meals in their backpacks will eat them without going to the dining room, which means no "legendary dining" happy thought, and you want your military dwarves to be happy. Turn off carrying rations in the military menu, or don't let them have backpacks to carry rations in. For the same reason, don't build chairs outside your dining rooms, except as needed by nobles, and never build a chair without a table next to it ("lack of tables" unhappy thought).
Personal rooms - Dwarves that have their own furnished bedroom often get happy thoughts such as "slept in a fine bedroom recently" and "admired own bed/cabinet/chest/door recently". You can also lock unhappy dwarves in their rooms when they go to bed by forbidding passage on the door, and force them to spend more time admiring their own fine beds, etc. (just try to keep them from starving/dehydrating in the process).
Statuary - Statues are some of the most valuable furniture that you can place around the fort, even a -statue- can give dwarves powerful happy thoughts. Lining corridors with statues and establishing statue gardens can often lead to dwarves admiring "a completely sublime statue recently". Why looking at statues of goblins striking down dwarves makes them more cheerful is anyone's guess.
Wells - Dwarves that need to wash off contaminants or are tired of booze will get annoyed if they have to use water from a stream/river/pool instead of well water, being "annoyed by the lack of a well recently". More than that, though, if you've gotten any masterwork or artifact buckets, chains, ropes, or mechanisms, it's very easy to create a "completely sublime well", especially if you have a skilled architect or mason, that can design/construct a masterwork well. Setting it as a meeting place from the (q) menu will lead to it also getting admired by jobless dwarves that don't need water. If you don't have any quality ropes or buckets, I'll bet using gold or steel blocks to build the well would go a long way toward making it sublime, too.