A Goggle search led me to their website and this page from their history:

Known Regimental Dead at Vicksburg, MS
(KIA = Killed in Action, DOW = Died of Wounds, DOD = Died of Disease, DUC = Died of Unknown Cause)

- Private Beverly Amos (Co K) KIA/DOW June 30
- Private Emanuel Antley (Co A) DOD July 2
- Private Benjamin Bryan (Co C) KIA June 11
- Private Henry Bryan (Co C) DOW June 29
- Private Hughey F. Cooley (Co B) KIA June 29
- Private J.M. Floyd (Co F) KIA
- Private G.B. Franklin (Co C) WIA/DOW May 22
- Private Andrew J. Grantham (Co C) KIA May 21
- Private Ephriam Hammock (Co B) KIA "in trenches"
- Private Matthew Hammond (Co I) KIA
- Private Nute Hammonds (Co G) KIA
- Private Mark Holton (Co A) on list of KIA, DOW, DOD
- Private James W. Ivy (Co C) KIA May 31
- Private Joseph Jarrell (Co I) DUC June
- Private Joseph Jones (Co K) DOW June 25
- Private Toliver Jones (Co I) DOW July 13
- Private Richard Kent (Co G) DOW - shot in collar, died in hospital
- Private Matthew Kerby (Co K) KIA/DOW
- Private Johnathan Logan Kerr (Co B) KIA
- Private David Kilpatrick (Co C) DOW/DOD July 15
- Private James H. Lett (Co I) DOW June 6
- Private B.G. Merrell (Co C) KIA June 12
- Private Miles Moore (Co I) DOW
- Private George Nunn (Co I) DOW
- Private Stephen Seats (Co B) KIA
- Private W.H. Sessions (Co F) DOD
- Private John T. Shaver (Co I) DOW
- Private William W. Shaver (Co I) DOW/DOD July 21
- Private Flavis G. Singleton (Co E) KIA
- Private Hamilton A. Stanley (Co H) KIA
- Private Thomas N. Tucker (Co I) DOD July
- Private Gideon Wall (Co C) DUC June 17
- Private Edmun G. Welch (Co B) KIA
- Private Henry B. Wooddy (Co I) DOD May 8
- Private Thomas P. Wright (Co F) DUC May 20

- Private James Wynnes (Co K) KIA

http://alabama37th.com/History-e.htm