It would appear that the 2nd Georgia State Guard morphed into the 37th District Georgia Militia at some point.

Piecing together a bunch of records, I found these:

W. Hearn, 4th Lieutenant, Company C, 37th Georgia Militia Regiment, present at the Post of West Point, Ga. January, 1865 [First I ever heard of a Civil War 4th Lieutenant, misprint?]

D. Martin, 3rd Lieutenant, Company C, 37th Georgia Militia Regiment, present at the Post of West Point, Ga. January, 1865

W T. Mooty, 2nd Lieutenant, Company C, 37th Georgia Militia Regiment, present at the Post of West Point, Ga. January, 1865

S. G. Tally, 1st Lieutenant, 2nd Lieutenant, Company C, 37th Georgia Militia Regiment, absent on 12 day sick certificate dated January 20, 1865

D. J. Statum, Major, absent on 60 day sick certificate dated December 14, 1864, hand written notation, crossed over 2 Ga ?r S. G.

D. J. Statham, Private, Capt. Cato's Co. (Chattahoochee Guards), Willcoxon's Regiment, Georgia,* joined for duty and enrolled August 9, 1863 at Lagrange, Ga. by Capt. Cato for 6 months, mustered out January 31, 1864, Camp near Rome, Ga.

.....

J. W. Akers, Quarter Master Sergeant, 37th District George Militia, signed a requisition for forage for 2 horses, August 4th, 1864 at West Point, Ga., W. W. Cato, Lieut. Col. Commanding

.....

William W. Cato, Captain, Capt. William W. Cato's Co. (Chattohoochee Guards, Troup County)* in the Reg't commanded by Col. John B. Willcoxon, for local defense, joined for duty and enrolled August 9, 1863 at Lagrange, Ga. by Capt. Cato for 6 months, mustered out January 31, 1864, Camp near Rome, Ga.

* This company subsequently became Company K, 2nd Regiment Cavalry, Georgia State Guards

William W. Cato, Lieutenant Colonel, 37th Georgia Militia Regiment, present at the Post of West Point, Ga. January, 1865, notation, Assigned to duty Gen'l Smith

M266: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Georgia, Miscellaneous File