Seing the eagle with shield and the letters CG on it, your guess is understandable, but it definitely is not a Coast Guard button (whose eagle is very different).
I could not find your unidentified button anywhere in the Tice button-book. However, your button is shown in the Albert button-book in the "Unclassified and Unidentified" section as Button #UU-18. It MAY be a slight variation of the City Guards of Boston (Massachusetts) button, shown in the Albert book as button MS-56 ...or MS-85, the Clinton Light Guards, also of Massachusetts.
I'll include a photo of MS-56, the City Guards (of Boston) button.
According to the McGuinn-&-Bazelon book on backmarls, your button's RMDC (Raised-Mark-in-Depressed-Channel) backmarks saying "Horstmann Bro. & Allien N.Y." dates it to sometime between 1850 to 1860.