I put a Kennedy $.50 on my daughters when she was a baby hers went in with no problem...

I know I put a cotton ball and athletes tape on mine but I wouldn't want to do the tape on newborns skin but maybe a cotton ball and bandaid. It doesn't really take it away but it helps it from popping out, but I think the only real thing would either be time or surgery. He might have an umbilical hernia or maybe his stomach muscles didn't close all the way