Reduce Overcrowding
Your "Viva Pinata" garden has limited space, and too many pinatas, plants and decorations can make your creatures miserable. Size is also a factor: An Elephanilla takes up much more space than a tiny Flutterscotch. You won't be able to add more items to your garden when you've reached maximum occupancy, and you may notice more fights among your pinata residents. Sell items from your garden, such as decorations, fruit that has fallen from trees and trouble-making pinatas, to reduce overcrowding.
Separate Natural Enemies
Some pinata species, such as Lickatoads and Newtgats or Raisants and Buzzlegums, are natural enemies, and they'll fight whenever they run into each other in your garden. Sadly, the only surefire way to prevent fights between these species is to keep them in separate gardens. Enter the village and go to the post office, then buy an empty crate. Pack all the pinatas from one of the species into a crate and mail it to yourself. Start a new garden and accept the crate from the post office. Unpack your pinatas in a fight-free environment -- for the time being, at least.
Build Fences
If you want to keep all of your pinatas together in a single garden, build a pinata pen to separate the warring species. Costalot's Store sells plain, inexpensive fences and fancier, more decorative pens. Connect all lengths of the fence so that no pinatas can get in or out, then place your pinatas inside. Give your pinatas enough space to roam around inside their pen. If you install a gate on your fence, keep it closed at all times. A pinata pen will protect your land pinatas, but won't have an effect on pinatas that can fly.
Increase Happiness
If a single pinata is picking fights with pinatas of multiple species, it may just be unhappy. Enter the pinata's information screen and give it a personalized name to increase its happiness. Aquatic pinatas like to be sprinkled with water from your watering can, and this is sometimes effective in putting an end to a fight. Costalot's Store sells happy candy that greatly improves a pinata's mood, and the joy candy sold at Ivor's Bargain Store brings a pinata to maximum happiness. Accessories, such as shoes and hats, also provide a boost to happiness.