Pokemon don't really have any favorite berries.......they're digital.
Chat with our AI personalities
The red shard can be given to the guy next to the Pokemon center for a cheri berry,a pecha berry and a leppa berry.
Give them a Bitter berry, play the poke flute,or give them an awakening
If you give them a oran berry, it will eventually turn into berry juice by a certain amount of steps. if you can keep the shuckle from using the berry juice, then after another amount of steps ( i have no idea how many) it will turn into a rare candy
After catching or defeating the Sudowoodo, a lady from the Flower Shop will give you the Berry Pots item. The Berry Pots allow you to plant berries inside of them. She'll also give you 3 Oran Berries and 3 Pecha Berries to get you started.
I believe the maximum number of berry pots you can have is four. I have SoulSilver, and I've beat it (except for getting the extra legendaries besides Lugia, Ho-Oh, and Groundon, and Dialga... through trading).