I asked this question around two months ago. I have since completed this game twice and I can confirm that there's an unlimited availability for all upgrade stones, each playthrough.
The hardest ones to get are definitely the slabs.
Regular Titanite Slab is a 100% chance drop off the Stray Demon, which you can battle on your second visit to Undead Asylum. Another slab is awarded for completing the Siegmeyer of Catarina sidequest. Although Titanite Slab is a rare drop off Crystal Lizards in the Great Hollow, it can also drop from Darkwraiths in New Londo Ruins, which respawn, making the supply unlimited.
Red Titanite Slab can be found in the Chaos Eater pit in Lost Izalith as a treasure to loot. It is also a rare drop off the Chaos Eaters themselves.
Blue Titanite Slab is found in the Crystal Caves as a lootable item. It is also a rare drop off the Crystal Butterflies in the same area, which respawn.
White Titanite Slab is found in the cave filled with Pinwheel Servants on a lootable corpse. It is also a rare drop off the Pinwheel Servants themselves.