Dear Mr. Bracey,
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The information you seek may be contained in his Individual Deceased Personnel File (IDPF). IDPFs from 1940-1976 for U.S. Army personnel with surnames that begin with A-L are in the custody of the National Archives at St. Louis (RL-SL). For more information about these records, please contact RL-SL via email at firstname.lastname@example.org.
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According to FamilySearch.org's Georgia, Death Index, 1933-1998:
Alfred J Guyer
30 Oct 1963
Ft Benning, Georgia
Birth Year (Estimated)
For a copy of the death certificate, you would need to contact the Georgia Health Department, Office of Vital Records, Atlanta. They may have qualifications you have to meet to be able to order the document.
Newspapers.com has the 02 Nov 1963 issue of the Brattleboro Reformer (Brattleboro, Vermont). It mentions Pvt. Guyer’s death on page 13. You would need a free trial, paid subscription, or free access through some libraries, etc.