What could the Supreme Court have done more constructively during Reconstruction after the Civil War to unite the North and the South.

I would like to take another angle on this question, as
some decisive action by the Supreme Court - or any action at all - could have made a
difference in the immediate postwar period.  The Black Codes, for example, were sets of
laws passed from county to county that put a large number of restrictions on free
blacks.  It limited their ability to travel, to own property and required they work for
a white person.  All of these were clearly unconstitutional, violations of the 13th and
14th amendments the country had just adopted.  The Court could have struck down these
provisions, and the Congress could have funded enforcement of the
rulings.

This was unlikely, given the conservative nature
of the Court during Reconstruction, and the apparent unwillingness of northern
politicians or civil rights advocates to pursue legal challenges to such laws, but it
was possible.  The death of Lincoln and the abolition of slavery itself took the steam
out of most of the civil rights efforts of the time.  Nevertheless, the Court could have
taken a more active role in protecting the nation's newest
citizens.

Now, would this have unified the country itself? 
Not necessarily, but it wouldn't have divided it further either, as their inaction most
certainly did.