Nobody thought he ____ do that. He did it and very successfully.
I think either 'could' or 'would be able to" works here. Am I right?
If you had simply been given the first sentence, I would have agreed that both "could" and "would" were possible. However, the addition of "He did it, and very successfully" makes it more likely that the outcome (he did it and he did it very successfully) is perhaps a surprise and therefore it is likely that before it happened, people thought he was not capable of doing it, therefore "could" would be the appropriate choice.