A potential conflict would probably that one or the other fighting for something they want.
Explanation:
Such as the night wanted the people to stay awake during the evening to see its wonderful creation and to gaze on the beauty of the stars and moon. While day thought it wouldn't be possible and would be an obscured idea. And then they decided to give it a try, which turns out bad or do an agreement. And the rest is up to you.
Sorry if this isn't what you're looking for, it was kind of confusing reading the question.
