After searching the office stores and Hobby Lobby, I finally found silver aluminum push pins at Lowe's. They look significantly better than pushed pins that are clear or brightly colored and add to the overall antique look.
I cut the earring post off using wire cutters. Then simply dabbed a drop of E6000 adhesive to the top of the push pin and set the earring onto the glue. That's it.
I dressed up my cork board using heirloom jewelry I never wore, but now enjoy seeing every day. This makes a great gift too. Just head to your nearest thrift store and stock up on old jewelry.