How do I convince someone to give their rabbit to me?

I know a family that is constantly busy being out of the house and that is perfectly fine, but the only problem is that they have a sweet rabbit that they have little time for. She is not neglected but she is constantly cooped up in her cage. I feel really bad for her. I have mentioned that I really love their rabbit, but the mother tells me that the kids love her too much to ever give up. I have already taken one rabbit from them that they did not want, this new one is its replacement. How should I go about doing this?