This pretty much proves that once a kid drops nap there is nothing you can do to make them sleep! I tell parents this all the time but they seem to think if a kid gets bored or lays still long enough they will sleep! No they won’t
My own kids lay quietly in their beds with no entertainment and were fine for an hour. If nap time is longer than that you can maybe have an hour of laying quietly and then an hour of books or books on tape etc. I typically habe some sort of activity available for the second hour if they are not able to keep being quiet. There are also really cool “quiet bins” I saw on Pinterest. Maybe you could make those for the daycare to use? Each day there is a new bin of reuseable activities.