Every monster has at least four different things that they like. For every unique object that they like that's placed near them, that monster's happiness will increase by 25%. Placing two of the same item near a monster will still only increase happiness by 25%. For purposes of making other monsters happy, a Rare monster is the same as its normal version. For example, a Toe Jammer likes a Furcorn, and also likes a Rare Furcorn. If a monster is close to both the normal and Rare versions of a monster it likes, its Happiness increases only by 25%, not by 50%. How quickly monsters earn coins is based on their Happiness.
Normally, for something to increase a monster's happiness, the two objects must be placed side by side. However, purchasing a Unity Tree from the market (available at level 16) will allow you place decorations and monsters anywhere you like on islands, including into Storage or a Hotel, without affecting the monster's happiness level.
This list makes reaching 100% happiness a cinch!