How do I improve Happiness in my Fallout Shelter? [duplicate]

I am playing Fallout Shelter, and I do not know how to make everyone happy. I have tried getting a lot of Food, Energy, and Water, but that did not work. I have also gave them pets and bigger rooms but that does not work either. Do you have any advice?

Manned Radio room increase happiness by a fixed perecent, per person (charisma level, room upgrade) for the entire vault; then makes the entire vault less happy, by the same percent, when people leave the Radio room.

Certain pets also work similarly, if they have happiness as their trait; i.e. Poodles.

Successfully rushing production increases (afew seconds after) the happiness of all people in the room by 10% (failing decreases 10%). Rush success is effected by luck and the room skill. Switch rooms when chance for failure is too high.

Low health, being revived, and witnessing death, also lowers happiness.

You can increase happiness with a Radio Room or Pets, as mentioned in Demaresa's answer. Neither of these make a big difference, but they help.

Rushing rooms is more effective, but only if you succeed, and you can only rush production rooms, so that doesn't help dwellers in training rooms.

The best way to increase happiness is through reproduction. Getting a female dweller pregnant will increase both dwellers' happiness to 100%. If my happiness is lagging, I'll find the least happy male and female dweller, and put them in a Living Quarters with +Charisma outfits. If you do this with any new dweller you get, whether from the wasteland or from pregnancy, then you'll have >90% happiness pretty much permanently.

Once you get the dweller to 100% happiness, you can assign them in a training or production room. Their happiness will stay at that level until something causes it to go down. This is generally some sort of disaster like a fire. I usually have everyone in production rooms at or near 100% happiness, and everyone in training rooms (roughly half the vault) at or above 75%.

Note that there's no benefit to having 100% happiness in your vault. Anything over 90% gives you the maximum production boost. According to @Nelson, there is actually a disadvantage to having everyone at 100%, as this prevents you from completing the challenge for raising a number of dwellers to 100%.