Is 2p online co-op allowed for this?

I think a relay format of 3 people would be more fun....

Considering co-op is not part of the categories that make up these trilogy runs, probably not. Nothing is stopping you from doing that for fun though.

I was asking because 2p is listed for the games individually, so it made sense to me that 2p would be an option for the trilogy. I'm going to assume that there is no interest in it overall and that's why it doesn't exist.