The easiest thing to do, in my opinion, would be to keep the Bolsheviks from becoming a power. All you’d have to do is knock Lenin out of the picture before the Germans ship him over in April 1917. The Bolsheviks were never that popular throughout the country, and many of their number within Russia (including Kamenev and Stalin) were endorsing cooperation with the Provisional Government before Lenin showed up. Without Lenin, the Party could do no more that Caesar’s arm when Caesar’s head is off.
Having Kerensky survive 1917 is a trickier matter, however. At some point, there needs to be a reckoning between the two governments that appeared in Petrograd during 1917: the Provisional Government (with Kerensky and the Duma) and the Worker’s Soviet (a grab-bag of radical parties). To simplify a complex problem, the PG had the upper/middle classes and the generals, but not much of an idea of what to do, while the Soviet had the workers, the grunts, and a plan to call for an armistice. Still, there was plenty of crossover between the two groups, and the Soviet was known for the occasional strategic blunder. It took Kornilov’s attempted putsch in early September to fatally weaken the PG and give the Soviet the legitimacy it needed to take over.
Fortunately, some work could have been done a few months earlier that could’ve removed the revolt entirely. Suppose Kerensky’s June offensive, which ended in OTL in the total dissolution of the Russian army, was instead a mild success, with the Russians being able to defeat the Austrians and hold the line from German counterattack. Kerensky did introduce disciplinary measures that were more or less mirrored by the Bolsheviks a little over a year later, so it is not completely outrageous to imagine some more cautious planning allowing them to be used to their full potential. With this notch on their belt, the PG will probably look a bit better, thus starving the Soviet of some converts. Without Lenin and his earlier directives to lower-level agitators in the Soviet, the July Insurrection would probably not occur. With any luck, this should appease the conservatives that backed Kornilov enough that they persuade him not to rebel. The PG is saved.
In the immediate future, Kerensky’s biggest problems would be absorbing the Soviet, restoring order , ending the war. The first two could be done, with any luck, with the creation of some type of reform program. Promising land reform would probably be enough to gain considerable support from the Russian countryside and the Socialist Revolutionary party, which was far and away the most popular party in Russia, while outlining some type of constitutional government would be enough to placate the Kadets in the PG. However, despite his support for the Entente, Kerensky would have to end the war soon. The Russian army simply couldn’t take much more at that point, and the number of insurrections breaking out across the empire as the imperial system collapsed back in 1917 would need immediate attention. With any luck, an armistice is negotiated with Berlin by early 1918, probably resulting in a milder version of the Brest-Litovsk treaty being applied to Russia, at least until the German war effort collapses later in the year.
While the Germans would probably collapse by the end of 1918, I doubt that the Entente itself would survive much after that. Neither London nor Paris would be terribly pleased at Kerensky’s armistice, and would doubtless use it to marginalize Russia’s role in the post-war order. Kerensky, for his part, would probably be quite put out to discover that the Entente powers never had any intention of actually giving Russia control over bits of the Balkans or Istanbul. I also doubt that Wilson’s babblings on self-determination would do much to reassure Kerensky of the Entente’s good faith towards Russia.
After that, I really can’t say what would happen. Russia would eventually stabilize (well, as stable as it usually gets), but I seriously doubt Kerensky was the type of leader to step aside when his time was past. I’d expect a series of pseudo-republican autocratic governments for the next three or so decades, coupled with slower industrialization, frequent civil unrest, and growing isolation from Europe. Essentially, it would be Putin’s Russia on a gradual upswing, rather than an arrested decline.