You have three choices:
1) Ignore the quest until further notice.
2) Spiritbond and convert gear of suitable level until you get some materia of the right sort - can be combined with letting Mutamix convert materia for you
3) Make enough money so that you can afford to buy on the market.

Now, as far as I know there is only one type of quest that ask for 2 Tier III materia - and that's the initial quest for the level 50 relic weapon.
At level 50 you should easily be able to afford two such pieces unless you have been wasting all the money you earned while getting there, or if everyone selling them are asking way too much for them