Raising a dweller's happiness

Solution 1:

Happiness can be positively affected by several things, primarily (but not restricted to):

Mating. This will automatically raise a dweller's happiness to 100%.
Successfully rushing a room. Raises happiness by 10%
Healing a dweller. This will raise a dweller's happiness back to their original happiness. I.e. if a dweller's happiness was at 50%, they then took damage/radiation poisoning, which lowered their happiness, they will return to 50%^{[citation needed]}
The Radio Room*. This automatically raises vault-wide happiness.
Bottle and Cappy*. The Nuka-Cola mascots occasionally visit your vault (if you have completed the "Nabbed from Nuka-World" event) and raise vault-wide happiness for a short time.

Happiness can also be affected negatively in several ways as well, including:

Dying. This can severely affect dweller happiness, often causing it to drop to minimal levels
Failing a rush. Unsuccessfully rushing a room can cause dwellers to lose 10% happiness.
Getting sick/injured. Taking large amounts of damage or radiation poisoning can cause dweller happiness to drop.
Not enough food/water. If the vault supply stores drop below the minimum requirements, vault-wide happiness will be reduced. This may also be applicable to losing power.
Dead bodies. If a dweller has died in a room, all other dwellers in that room will lose significant levels of happiness. (May affect vault-wide happiness).

*Sources needed for how much these affect happiness.