The most straightforward way is for Johnston and
With any POD beginning in January 1862, cause a major battle at Memphis between the army of West Tennessee and the Army of the Tennessee sometime in 1862 with the army of West Tennessee defending Memphis from a Union assault.
The most straightforward way is for Johnston and Beauregard to hold off from the attack at Pittsburg Landing/Shiloh, although basically surrenders the initiative to Grant ... which means, presumably, he takes command at the Landing, consolidates the entire army (six divisions) and then moves either:
a) southeast to connect with Buell's Army of the Ohio to take Nashville, or
b) southwest, possibly a mix of overland movement and/or the rivers (back out to the Ohio,then south along the Mississippi)
The problem that presents for the rebels, of course, is that they didn't have any answer for the US naval strength on the rivers, even in 1862; likewise, since the rebel intent was to try and defend Nashville by attacking at Shiloh, then remaining on the defensive at Memphis is going to do even less than Johnston's historical strategy.
The option is to split the Army of Tennessee and try and defend both Memphis and Nashville, but that basically puts the rebels into the same situation they were historically, with a single force that is essentially outnumbered - even separately - by both Grant's force and Buell's...
Johnston had (roughly) 45,000 troops in the field at Shiloh; Grant alone had 49,000, and Buell brought another 18,000 to the battle. And those forces were far from what was available; according to the Official Records, on Feb. 15, 1862, the US forces in the Western theater(s) included:
Department of the Ohio – 92,221 troops
Department of the Missouri (Halleck, so including Grant's) – 108,905 troops.
Basically, the US forces in the theaters by the first quarter of 1862 numbered ~200,000; even including the rebel forces in eastern Tennessee or in Missouri (to make it analogous to the two US departments listed above) it's a safe presumption that the US forces outnumbered the rebels by at least 2 - 1, if not more, and not including the naval forces.
Best,
