I find no reference to the "Conasauga Volunteers", although it may have been a Militia unit which became Co "H" of the 19th TN Infantry Regiment.

Cobb, D.A. TN 19th Inf. Co.H
Cobb, B.P. TN 19th Inf. Co.H
Cobb, Jesse M. TN 19th Inf. Co.H
Cobb, W.J. TN 19th Inf. Co.F Cpl.

and you are right, the 19th was at Mill Springs, KY on Jan 19, 1862. The 19th had organized at Knoxville on June 11, 1861.

As for "COBB" of Tennessee, there was a Major Pharoah A. Cobb with the 2nd TN [Ashby's] Cavalry Regt.
Cobb, P.A. TN 2nd (Ashby's) Cav. Co.E Maj.
Cobb, P.A. TN Cav. 4th Bn. (Branner's) Co.D 1st Lt.

Other COBB's of TN:

Cobb, A.J. TN 2nd (Ashby's) Cav. Co.E
Cobb, Andrew TN 43rd Inf. Co.E
Cobb, Andrew TN 9th Inf. Co.K
Cobb, C.L. TN Cav. 16th Bn. (Neal's) Co.B
Cobb, C.W. TN 1st (Carter's) Cav. 1st Lt.
Cobb, Charles E. TN 25th Inf. Co.A
Cobb, Clisby TN 26th Inf. Co.F
Cobb, Edwin B. TN 14th Inf. Co.H
Cobb, Ellis TN 20th (Russell's) Cav. Co.E
Cobb, F. TN 12th (Green's) Cav. Co.I
Cobb, G.A. TN 18th (Newsom's) Cav. Co.A
Cobb, George A. TN 14th Inf. Co.E
Cobb, George A. TN 19th & 20th (Cons.) Cav. Co.C
Cobb, George L. TN 2nd (Robison's) Inf. Co.F
Cobb, H.B. TN 4th Inf. Co.H 2nd Lt.
Cobb, Henry L. TN 14th Inf. Co.D
Cobb, I. TN 42nd Inf. 2nd Co.E 2nd Lt.
Cobb, I.D.C. TN Cav. Nixon's Regt. Co.A
Cobb, Irwin I. TN 50th Inf. Co.F
Cobb, Isaiah TN 40th Inf. Co.C 1st Lt.
Cobb, J.A. TN 55th (Brown's) Inf. Co.G
Cobb, J.C. TN 5th Inf. 2nd Co.K
Cobb, J.C.W. TN 7th (Duckworth's) Cav. Co.L Sgt.
Cobb, J.D.C. TN 15th (Cons.) Cav. Co.C 1st Sgt.
Cobb, J.D.C. TN 15th (Stewart's) Cav. Co.A 1st Sgt.
Cobb, J.E. TN 14th (Neely's) Cav. Co.D
Cobb, J.F. TN Inf. 154th Sr.Regt. Co.I
Cobb, J.H. TN 4th Inf. Co.E
Cobb, J.N. TN 40th Inf. Co.E
Cobb, Jacob TN 4th (McLemore's) Cav. Co.E
Cobb, James TN 1st (Carter's) Cav. Co.C Far.
Cobb, James TN 38th Inf. 1st Co.K
Cobb, James TN Cav. 11th Bn. (Gordon's) Co.F
Cobb, James A. TN 34th Inf. 2nd Co.C
Cobb, James C. TN 1st (Turney's) Inf. Co.H
Cobb, James G. TN 19th (Biffle's) Cav. Co.B
Cobb, James N. TN 2nd (Robison's) Inf. Co.F
Cobb, Jesse TN 4th (Murray's) Cav. Co.D Cpl.
Cobb, John TN 7th (Duckworth's) Cav. Co.M
Cobb, John B. TN 1st Cav.
Cobb, John B. TN 59th Mtd.Inf. Co.H Capt.
Cobb, John S. TN 37th Inf. Co.E
Cobb, Joseph TN 14th (Neely's) Cav. Co.C
Cobb, Kedar O. TN 40th Inf. Co.C Sgt.
Cobb, L.D. TN 14th (Neely's) Cav. Co.I
Cobb, M.D. TN 1st (Feild's) Inf. Co.L
Cobb, M.D. TN Inf. Nashville Bn. Felts' Co.
Cobb, M.T. TN 30th Inf. Co.A
Cobb, Marion Price TN 1st (Turney's) Inf. Co.E
Cobb, Oliver TN 42nd Inf. 2nd Co.E Sgt.
Cobb, P.F. TN 19th (Biffle's) Cav. Co.B
Cobb, Philip TN 3rd (Clack's) Inf. Co.I,K
Cobb, R. TN 42nd Inf. 2nd Co.E Sgt.
Cobb, R.H. TN Inf. 154th Sr.Regt. Co.I
Cobb, R.J. TN 6th (Wheeler's) Cav. Co.K
Cobb, R.J. TN Cav. 11th Bn. (Gordon's) Co.A
Cobb, R.M. TN 38th Inf. 2nd Co.A
Cobb, Robert L. TN 50th Inf. Co.A,F 2nd Lt.
Cobb, Rufus TN 18th (Newsom's) Cav. Co.A
Cobb, S.A. TN 7th (Duckworth's) Cav. Co.L
Cobb, S.P. TN 14th (Neely's) Cav. Co.F
Cobb, S.R. TN 40th Inf. Co.C Sgt.
Cobb, S.U. TN 63rd Inf. Co.B
Cobb, Samuel TN 4th (McLemore's) Cav. Co.E
Cobb, Samuel U. TN 26th Inf. Co.F
Cobb, Seymore TN 37th Inf. Co.E
Cobb, T.C. TN 1st (Feild's) & 27th Inf. (Cons.) Co.D 2nd Lt.
Cobb, T.C. TN Inf. Nashville Bn. Felts' Co.
Cobb, T.J. TN 40th Inf. Co.E
Cobb, Theophilus T. TN 37th Inf. Co.E
Cobb, Thomas C. TN 1st (Feild's) Inf. 2nd Lt.
Cobb, Thomas C. TN Inf. 1st Cons.Regt. Co.B 2nd Lt.
Cobb, W.A. TN 14th (Neely's) Cav. Co.F
Cobb, W.A. TN 6th Inf. Co.K
Cobb, W.C. TN 6th Inf. Co.A
Cobb, W.C. TN 7th (Duckworth's) Cav. Co.M
Cobb, W.P. TN 14th (Neely's) Cav. Co.F
Cobb, W.R.W., Jr. TN 34th Inf. Co.K Bvt.2nd Lt.
Cobb, W.T. TN 7th (Duckworth's) Cav. Co.L
Cobb, William TN 14th (Neely's) Cav. Co.C
Cobb, William TN 3rd (Clack's) Inf. Co.I,K
Cobb, William B. TN 1st (Turney's) Inf. Co.H
Cobb, Willis M. TN Cav. 11th Bn. (Gordon's) Co.B

Information taken from the Roster of Confederate Soldiers, 1861-1865.

You might want to try contacting
Tennessee State Library and Archives
403 7th Avenue, North
Nashville, TN 37243-0312
615-741-2764