Candary, Juicygoose, Salamango and Zumbug
You evolve these pinatas when you feed certain food items to a pinata of the origin species. Feed a buttercup to a Sparrowmint to get a Candary, give a gooseberry to a Quackberry pinata to get a Juicygoose, feed a chili to a Newtgat to evolve it into a Salamango and feed both a blackberry and a daisy to a Horstachio to get a Zumbug.
Flutterscotches
The white flutterscotch, unlike other pinata species, doesn't have color variants. Instead, it evolves into nine other species. Only white flutterscotches evolve. Feed a white flutterscotch a bluebell to get a blue flutterscotch, a tulip to get a black flutterscotch, a poppy to get a red flutterscotch, a buttercup to get a yellow flutterscotch, a bullrush to get a brown flutterscotch, a watercress to get a green flutterscotch, a water lily to get a pink flutterscotch, a bird-of-paradise to get an orange flutterscotch and a thistle to get a purple flutterscotch. Each type of flutterscotch can only be romanced with another of the same color, but you can get romancer and master romancer awards for all 10 types.
Lackatoad, Reddhott and Chocstrich
To get a Lackatoad, feed a Lickatoad a nightshade berry. Normally, this would make the pinata sick, but if you whack it with your shovel after it eats the berry, it evolves into a Lackatoad. To make a Reddhott, you need a Taffly pinata and a firebrand, which is sold by Costolot's Store. Direct the Taffly into the flame on the firebrand. After it catches fire, use your watering can to douse it, and you'll have your own Reddhott. The Cluckles is a domestic pinata that you can only get from the Paper Pets store in the village. Buy a Cluckles and feed it two cactus seeds to get a Chocstrich.
Twingersnaps and Fourheads
These serpents both evolve from the Syrupent. After you romance two Syrupent pinatas, wait for the stork to bring the egg to the Syupent house. The egg bounces gently on its perch while it's incubating. When it makes three high bounces, hit it with the shovel. The egg will hatch a two-headed snake, the Twingersnap. If you romance two Twingersnaps and hit the egg, you'll get a Fourheads pinata.
Pieena, Polollybear, Parmadillo, Moojoo and Hoghurt
These pinatas only appear in "Trouble in Paradise." Feed a fir tree seed to a Doenut to get a Moojoo, give a blue gem to a Fizzlybear to evolve a Polollybear, feed a coconut to a Fudgehog to evolve it into a Parmadillo and feed a bone to a Pretztail to get a Pieena. The Hoghurt evolves from a Rashberry, another domestic pinata, when you feed it cheesecake. Get Bart from the village to tinker milk into cheese, then hire him to tinker the cheese into cheesecake.