I'm not great at writing, but I do know my animals. I have a few suggestions.
Sheep Oak Handle Tanto Grandma and grandpa's first meeting. One of grandmother's sheep gets tangled up in some briars/a net/ whatever seems plausible, and grandfather shows up and cuts the sheep loose. They fall in love. Could also work for rabbit, boar or horse.
Tiger:Okay the tiger story has to be about Meili. Maybe grandmother and her friends used to pretend they were gods, and grandmother always wanted to be Meili, but they wouldn't let her because she was a girl. So HER grandmother got her the tiger slippers, and taught her a lesson about being confident in yourself. Or something?
Dog: Straw HatGrandmother goes to the river on a hot, sunny day and almost drowns. Dog saves her, but she loses her straw hat.
That's all I got for now. Need to do more research.
Edit: I'm on mobile now so I can't link to items, sorry.
Chicken: Festive treat basket
Grandmother is collecting eggs. She sees a rooster protects his hens from a fox.