Black belly button. Will the color change or is there something that can be done to fix this now? (Photo)

There is nothing that should or could be done at this point.  Things will heal over time.  The color may or may not change.

Thank you for the picture. Unfortunately it looks like your bellybutton is very unhealthy and lacks circulation. This needs to be read it or cleaned out down to healthy bleeding tissues and treated conservatively with local wound care. Please see your plastic surgeon as soon as possible. 

There's really not much to be done now even if the umbilical stalk has inadequate blood supply. More than likely this is temporary discoloration but should be followed by your surgeon.