I have a child who periodically starts wailing. She does this at home, also. The best solution I've found is to say, "I'm sorry you're sad. You can come sit with me if you'd like to be quiet and sad. If you need to be loud and sad, you can do that in the quiet corner." She always picks the quiet corner!
Children have different temperaments. Many do NOT want to be physically comforted; they need time to express their sadness and don't want to be grilled about the root of their feelings when they don't even know what that root is. Our job as care providers is to first see if there's an immediate physical reason for the tears, then do what we can to make the child comfortable during the duration of the crying fit so they're able to process those feelings.
As adults, we understand this about ourselves; don't you feel frustrated and misunderstood when you get upset in front of a spouse or friend, and that person tries to FIX you instead of giving you space to have those strong feelings?
Different kids need different kinds of comfort. Sometimes, giving them space and letting them see the activity going around them will draw them right out of their sadness.
Also: For some children, crying becomes a method of getting positive attention from their parents. If day care providers shower the child with extra attention when the child cries, then they've reinforced the idea that "crying makes me happy." That's a terrible lesson to learn.
We give cuddles and conversation when those kids are NOT crying.