A class has particularly enjoyed a film and want to see it again. Could they ask their teacher: "Could you play it again please?"
Could they ask their teacher:
"Could you play it again please?"
Of course they can. I don't see why not. To me, this is perfectly idiomatic. But how children ask this really depends on their understanding of the language and their age, I guess. If they are too young, they may just say "again".
They could also say:
"Could you replay it, please?"
And they could also say:
"Could you show it again, please?"
In this very straightforward case, both "can" and "could" work equally well.