I have a copper-topped table that has a rich oxidized finish. 
Accidently two small spots became clean and the bright copper shows
through.  Is there a way to speed the oxidization process so the
tabletop finish can be uniform again?

Chlorine bleach will tarnish copper. You might try dabbing the spots
with a cloth that has been dipped in a dilute solution of Clorox (or
its equivalent).