Is there a UPS or FexEx shipping center at the Miami Airport where I could ship a second bag home rather than paying the airline fee?

Are you sure the mailing charge (by FedEx or UPS) will be less than the 2nd bag fee?

Looks like there is a full service Post Office at the Airport.
http://www.miami-airport.com/html/services_at_mia.html

I must agree with yk, I can't imagine that shipping a bag would be cheaper than $15 or whatever your airline charges. Besides, by shipping the bag it will take God knows how long to reach you. When you check the bag you will get it when you arrive at your destination.

(OK, presumably the bag will arrive when you do) ;-)

There used to be a fully staffed, 24-hr US post office at one of the terminals (anybody know if it's still there)

There is a link to the post office in the first response.