Don't know the show or size of your barn doors in question, but if they
are already being/have been built, Krylon spray paint has a full line of
metallic paints of every kind, including copper, gold, silver, etc. With
a coating of good metallic copper paint, an added sealant of clear spray
lacquer, varnish, or polyurethane over the copper paint will give a
realistic metallic sheen to your finished work. Just be aware that there
are many paint companies that supply these types of finishes. Go online
and start searching.

Others on this NG will have good ideas about paints and treatments, so
consider their ideas as well. There are some very skilled artists and
scene shop technicians here who will have great suggestions for you.

Reagards,
Bert