"De nouveaux manteaux"
because of the adjective between the partitive article and the noun. It would have been "des manteaux jaunes" It is not a cast iron rule, but use it and it will save a lot of irritation with duolingo.
Yes, it's best to go on like siebolt said. We had a lengthy in detail discussion of the topic some months ago with lots of quotes from all sorts of dictionaries. Unfortunately, I can't find it anymore.
I'm wondering about this, too. The pronunciation of nouveau manteau and nouveaux manteaux is the same (at least to my ear). How are we supposed to know which form (singular or plural) follows de?
Or is it because de here means "some"? That if it's singular it would be un nouveau manteau?