As you're playing through the game you should get a lot of berries thrown at you, especially by Pokemon Rangers. And that should help you get started when breeding, which isn't too hard, but will take awhile. Keep in mind though that a lot of berries that can also only be found in X and Y by destroying the Berries Trees that sometime appear during battle in certain areas, by using either Hurricane, Blizzard or Twister.
There are six colors of trees and each will drop one of several possible berries that fall under that color group.
Green Berry Trees
Drop either: Rawst, Lum, Aguav, Rindo Kebia, Tanga and Babiri.
And can appear in any battle on: Route 5, 6, 7, 10, 11, 18 (west), 19 (west), 22 or the Pokemon Village
Purple Berry Trees
Drop either: Chesto, Wiki, Payapa, Kasib or Colbur.
And can appear in any battle on: route 5,6, 7, 10, 11, 18 (west), 19, 22, or the Pokemon Village
Yellow Berry Trees
Drop either: Aspear, Sitrus, Iapapa, Wacan, Shuca, Charti or Chilan
And can appear in any battle on: route 8 (in the grass and flowers), 9, 13, 18(east) or 19 (east)
Red Berry Trees
Drop either: Cheri, Leppa, Figy, Occa, chople, or Haban
And can appear in any battle on: route 8 (on the beach), 12 (on the beach), Ambrette Town, Cyllage City, Shalour City or Azure Bay
Blue Berry Trees
Drop either: Oran, Passho, Yache or Coba
And can appear in any battle on: Route 17 or the outside area of the Frost Cavern.
Also there are two berries that can only be found by getting 100 and 200 straight wins in the Battle Maison. These are the Lansat and Straf respectively. They take a substantial amount of skill and Patience to earn though. So you may find them easier to just trade for them. These two are particularly useful since you can mix them at the juice Bar to make Rare Soda, which raise a Pokemon's Level by 1-4.
