Go to the Omega ruins and fight Machea. You'll get a couple for defeating them. Either that or Mana spheres. Anyway, just keep doing this and you'll get some.
Another way is to capture a Varuna from the Omega ruins and fight it in monster arena. I noticed that it dropped Lv. 3 Key Spheres about 50% of the time. You also make a 1000 gil profit if you equip Rikku's Godhand.
If you're stuck in Zanarkand though you might want to just forget about it for now and do it later. That's what I normally do.