From The Life of Mark Twain: The Early Years, 1835-1871, pp127-8

Steamboat: SUNSHINE
Built: 1860
Tonnage: 354
Clemens' Service: 6 December 1860 - 8 January 1861
Pilot: Capt. George W. Willard in 1860; Absalom Grimes in 1861
Captain: Henry G. Carson
Fate: burned 13 July 1864 in St. Louis by Confederates

Steamboat: ALONZO CHILD
Built: 1857
Tonnage: 493
Clemens' Service: 19 September 1860 - 18 November 1860
and 8 January 1861 - 8 May 1861
Co-Pilots: Horace Bixby, William Bowen, Sam Brown
Captains: David DeHaven and James O'Neal

Steamboat: ARAGO
Built: 1860
Tonnage: 268
Clemens' Service: 28 July - 31 August 1860
Co-Pilot: Isaiah W. "Bill" Hood
[identification of "Bill" Hood was made by researcher Michael Marleau, Nov. 2006]
Captain: George P. Sloan
Fate: Burned in Dog Tooth Bend, near Commerce, MO on Feb. 6, 1865.

Steamboat: CITY OF MEMPHIS
Built: 1857
Tonnage: 865
Clemens' Service: 25 March - 1 or 2 July 1860
Co-Pilot: Wesley Jacobs
Captain: Joseph Edward Montgomery
Fate: boilers exploded May 31, 1866 with loss of eleven lives; towed to Saint Louis, MO and dismantled

Steamboat: A. B. CHAMBERS
Built: 1855
Tonnage: 410
Clemens' Service: 26 October 1859 - 24 February 1860
Co Pilots: James DeLancey and William Bowen
First mate: Grant Marsh
Captain: George Bowman
Fate: snagged and sank near St. Louis, 24 September 1860

Steamboat: EDWARD J. GAY
Built: 1859
Tonnage: 823
Clemens' Service: 2 August - 1 October 1859
Captain: Barton Bowen
Fate: 1863 acquired by Confederacy and taken up Yalobusha River; later burned on 17 July 1863 to prevent capture.

These dates were theorized by Branch for June 25, 1859 to July 28, 1859,  not corroborated by Marleau 

Edgard Branch, the source for Day By Day, had originally dated Clemens' service on the RUFUS J. LACKLAND as 11 July - 3 August 1857. Further research by Michael Marleau, includes a new interpretation of Clemens' personal journals and indicates the 1859 dates are the most likely dates of service for the RUFUS J. LACKLAND.   July 9 – July 30, 1859