Is there any way to get multiple copies of the gems?

Is there any way to get multiple copies of the gems (ie: Normal Gem) in one play through of the game? I’ve been trying to make some fun and unique pokemon combos and these gems would make my Unburden Hitmonlee better. Also any way to get multiple berries because those could work too?

Buying/acquiring other gems and berries might be added later on 1.2.

You can steal the Berry Juice off wild Shuckle.
Easy way to do this is get a Pumpkaboo with Frisk in friend safari and make it re-learn the starting move Trick.
Or get an Espurr in friend safari; it knows Covet already (no Frisk though, but all Shuckle carry a Berry Juice).

Thievery reference list (pretty sure it’s the Gen V one):
http://bulbapedia.bulbagarden.net/wiki/List_of_Pokémon_by_wild_held_item

You can also try trading for the gems. As for berries, there are a few scattered in the overworld throughout the game. In addition to that, there’s an NPC in Utira Town who gives a random berry each day.

Sonata tracks rewards should be fixed in 1.2 and one of the sponsors has a chance of giving you berries if you win.

And like Aboodie and Apophys said, more methods might be added in 1.2 or you can use a frisk pokemon knowing Covet/Thief/Trick/Switcheroo (Banette has frisk and eventually learns trick) and get berries from wild pokemon found in the routes(FS pokemon in insurgence don’t hold any items).