The two cent coin debuted in 1864 under the mint AG 08. That year it was struck in bronze as was the Indian Head of that year. The civil war was raging and coins were scarce because of hoarding. “Hard Money” was desired by the public. Production was increased in 1864, then mintage declined due to once hoarded Indian Cents being available action. Also the new nickel three cents were produced in 1965. Smaller quantities were made through 1872 then proofs only in 1873. Most coins were well struck. On the obverse check the leaves and the “we” in the note and the shield lines. Check the wreath details and border letters on the reverse. Also check the dentals on both sides.
Most mint state coins are dated 1864 or 1865 availability then declines rapidly especially the 1872 coins. Most 1864 coins have the large motto. Small motto coins are rare. In the market place most coins have been recorded. The original mint red-orange color are rare especially in later years. Happy hunting.