Ideally your sister would find out (any way at all you can persuade your niece? Why doesn't she want her to know?) and then the school would deal with it.
However, if they won't, you/she unfortunately need to take it into your own hands.
I agree with @DavidBeckhamsrightfoot - she needs to find a weakness and call them out on it.
"Becky, I might cry when people try to bully me, but you'll always be stupid and end up working for me".
"Selena, I might be easily upset by people making fun of me but my dad loves me, unlike yours, who left".
"Gemma, I might get upset when girls like you try to make my time at school miserable, but at least I have true friends who like me, unlike this group of cronies who I overheard calling you a bossy b1tch behind your back yesterday".
These might sound overly harsh, especially to a kind, sweet girl, but she needs to show she's just as willing to fight back as they are to bully, otherwise they'll carry on.
If she can't do it herself, would you be willing to go in and have a word with them yourself, at home time?