The Byron Reed example of the 1863 shield obverse design with motto 'God Our Trust' combined with the reverse with 2 Cents curved struck in bronze. These were apparently struck late in 1863 as per the following notation in George Eckgeldt's journal.
Examples exist in the following combinations:
Bronze & Copper J312 & J312A/P377 on multiple weight planchets ranging from 76 grains all the way to 101 grains. An example, donated by the U.S. Mint, has been in the British Museum since 1864. It would be interesting to see if there is anything in the Mint Archives regarding this.
One example is known with clash marks on the reverse from the Washington obverse of J305/P370.
Copper-nickel J313/P378 with about a half dozen known.
Aluminum J314/P379 which may be unique and is ex J.E. Drew, Simpson-Heritage 11/20 - PCGS65.
An obverse die trial lacking the date JA1863-1/P3257 is also known.
Photo from the Byron Reed Collection; owned by the City of Omaha, Nebraska; on loan to The Durham Museum.
Eckfeldt journal notation courtesy of Alan Meghrig.