I could find no record of the Conasuaga Volunteers in either Amann or Tancig (Listing of Confederate Company names).

The following units comprised Crittenden's command:-

16th Alabama: Col William B. Wood

15th Mississippi: Ltc Edward C. Walthall

17th Tennessee: Ltc Thomas C. H. Miller
19th Tennessee: Col David H. Cummings
20th Tennessee: Col Joel A. Battle
25th Tennessee: Col Sidney S. Stanton (w)
28th Tennessee: Col John Porry Murray
29th Tennessee: Col Samuel Powell (w), Maj Horace Rice

37th Tennessee: Col Moses White (engaged in the defense of Beech Grove)[not engaged]

1st Tennessee Cavalry Battalion: Ltc Frank Nathaniel McNairy (may have been present at Beech Grove)[not engaged]
3rd Tennessee Cavalry Battalion (2 companies): Ltc William Brazleton[not engaged]
4th Tennessee Cavalry Battalion: Ltc Benjamin M. Branner
5th Tennessee Cavalry Battalion: Ltc George R. McClellan
Tennessee Cavalry Company: Cpt William Scott Bledsoe
Tennessee Cavalry Company: Cpt Q. C. "Ned" Sanders (or Saunders)

Kentucky Cavalry Company: Cpt B. E. Roberts (attached to Bledsoe & Sanders)

Tennessee Battery: Cpt Arthur M. Rutledge
Tennessee Battery (Caswell Artillery): Cpt Hugh L. W. McClung [not engaged]
Tennessee Battery (Harding Artillery): Capt G. H. Monserratt, Cpt Ed Baxter[not engaged]

Perhaps someone with a knowledge of recruitment areas can suggest a possible unit

Alan Thrower
England