Often times a button maker would use a slightly different backmark for civilian buttons compared to military buttons. On your picture I can see an "A". That leads me to Amasa Goodyear (& Sons). The following came form "American Military Button Makers and Dealers; Their Backmarks & Dates".
Amasa Goodyear (& Sons), Waterbury (Salem Bridge), CT. Dated 1805-35 but possibly c.1800. Contracted to make Light Artillery buttons on Dec. 3, 1808. Made infantry white metal buttons in 1812. A letter of April 12, 1812 complained about the poor strikes of the letter "I" on these buttons. In Sept. he submitted samples of infantry buttons he proposed to supply. No b/m's are known to exist on these buttons but "A. Goodyear". (c 1815-c1821), "A. Goodyear & Son" (c1821, c.1826) & A. Goodyear & Sons (c.1826-c.1835) appear on plain pewter (Hard White) buttons. Goodyear was one of the founders of the New Haven & Baltimore Button Co. He also was the father of Charles & Nelson Goodyear, famous for work with hard rubber. (See Just Buttons Magazine, June 1977).