"Of whom" must be qualified by some sort of quantitative descriptor. "None," "some," "few," etc, or even an actual number, although that's less conventional.
You should add "some" in front of "of", but there's another minor problem: you've forgotten an article between "such" and "job".
I contacted a couple of suitable candidates, some of whom I thought would be capable of handling such a job, but unfortunately none of them were interested.
Be careful when you use commas with particular clauses like this, so that you don't create a comma splice.
Tunny's suggestion is close, but I think somewhat innaccurate. "Who" is a subject pronoun, and "whom" is an object pronoun, this is true. However, "that" is also used to refer to people, and "that" is used to denote an essential clause, which is the middle of your sentence between the commas.
(Edit: The second sentence of this paragraph shows how not to use commas... don't do that.)
I contacted a couple of suitable candidates that I thought would be capable of handling such a job, but unfortunately none of them were interested.
Essential clauses add vital information to the sentence. In this case, we wouldn't know what kind of candidates you were choosing. You can also remove the adjective "suitable" (or, alternatively, the whole clause in the middle) since they mean the same thing. In this particular case, the "essential" clause isn't actually essential because "suitable" implies that they would be capable of handling whatever job you're talking about.