Lawyer Alan Sklarsky, who represents hundreds of Paulsboro residents, says Conrail is offering some families $500 per child. Those closest to the derailment site are being offered more.
Sklarsky says the amount would not cover future medical bills if the children get sick.
One tanker released vinyl chloride into the air when a half-dozen rail cars derailed on a bridge in November. The chemical is linked to short-term breathing problems, but prolonged exposure has been tied to cancer.
Conrail has said that it is settling claims "fairly and promptly."
A judge has not yet ruled on the settlements.