there is a pretty rare chace of them hating each other, what you do is leave a male and a female pelipper at the daycare and they should breed, the old man outside the daycare will say weather they will get along or not, if they get along they will breed.
then you go for a walk and then after a while go to/past the daycare and he will call you or you can go and talk to him and he will give you the egg only if you have room in your party, or if you dont want the egg just say no and he will keep it.
to get the egg to hatch you wild need to walk alot and it will hatch.
I hope my answer has helped you ultra barx