1861-1865 is probably the best you can do Welcome to CT https://www.vcoins.com/en/stores/la..._a_our_navy_ngc_ms_63_bn/1329445/Default.aspx
PCGS shows 1860 - 1865! Here is the link! https://www.pcgs.com/coinfacts/coin/no-date-token-f-53-336-our-navy-rb/602589
For CWTs, you can't pin down an exact year, except that they were minted around the Civil War period. I've got only one CWT and it has the same obverse as yours! I'm not home for a clearer pic (this one's from my phone). Notice that both yours and mine have only 12 stars instead of 13? Not quite sure why. There are mainly two types: Store Cards and Patriotic Tokens (like both of ours). There's a website (cwtsociety.com) with tons of more info if you're interested.
Due to my health the best I can say is the US was only minting coins when the war broke out in 1861. The south minted a few but mainly went to paper money. The north stuck with the coinage. There were 2 southern tokens I believe but please don’t ask as I can not provide adequate information on that. Most of the tokens were from the north.
You might be able to narrow down the issue date if you can match the dies to other dies they may have been muled with, and if those dies are dated give you a narrower time frame. I don't have my copy of Fuld's patriotic tokens book readily available so I can't track down the dies. I believe the "Wealth of the South" token may have been struck in the south, but other than that I believe all of the Civil War tokens were struck in the north.
I am not sure of the date, You can look it up on this web page to find the die sinkers and rarity though. https://www.cwtoken.com/Civil_War_Token_Type_Set/Cent_Facsimile/Pages/I_-_Indian_Head.html
The vast majority of Civil War tokens were struck and issued in 1863. That one appears to be of that vintage. The 1861 pieces are few and far between. The 1862 pieces are the second most common, and the Union outlawed the use of the tokens in the first half of 1864. The Civil War collectors don't recognize any pieces from 1865 because that was after the laws that ended their use were passed. Here is something, with a similar obverse, which is dated 1864. There weren't any really good die sinkers in the South. The most famous pro-southern tokens were the Wealth of the South pieces that were made in Cincinnati, Ohio and issued starting in 1860. That group of tokens is the only Civil War Tokens that have an 1860 date. Everything else is dated from 1861 to 4. Here is an original Wealth of the South token. This is a rare variety which was sold to southerners just before the war began. Wealth of the South tokens continued to be made and sold during the war, more for collectors. Here is an example. This one was probably sold circa 1863. The reverse is the same for all of them, but the obverse die broke and was replaced several times.
Most all of the pro-southern tokens were made in the by or for "copperheads," northern southern sympathizers. Their message was subtle. For example. This piece stirs up resentment for contractors who sold war goods to the government while the soldiers' widows got very little. The Indian's headband reads "Fort Lafayt (Fort Lafayette), which was a fort in New York Harbor were those suspected southern sympathizers were imprisoned (often without formal charges) under harsh conditions. George Washington was taken as a hero for both sides. Here under what looks to be patriotic theme, the reverse calls for what the South wanted. Peace with the Southern states leaving the Union.
