Me too, ha ha! I tried putting it in English and they both sound fine to me.
The boy has promised me that he would go to the party. The boy has promised me that he will go to the party. So, I'm not sure, but in any case I don't care about the English, just the Spanish. (Sometimes putting it into English helps)
The reason I ask is because in a class, the teacher accidentally put this same question on the exam twice. For the first one I marked: "irá," and she marked it wrong. Then for the second one, I marked "iría," and she also marked it wrong, ha ha! (And there were only 2 options) Ha ha! Confusing...I think she just checked it way too fast. But in any case, that leaves me without knowing the correct answer.