Essentially, Materia doesn't work in the Synthesis Table. I have been trying to make a philosopher's stone for an hour, and it won't accept any amount of materia. I have tried using all types of materia from Tier A downwards, and nothing is working.

[PHILOSOPHER'S STONE SPOILERS FOLLOW]
The part of the Philosopher's Stone recipe that occurs in the Synthesis Table does not use materia dust, but rather an Activated Amaranth Pearl.

How do you get the cracked Amaranth Pearl? I've tried everything, but not cheating it in.

Try placing an Amaranth Pearl into a Calcination Furnace.