First, why is Kentucky so important to the outcome of the Civil War? It is said that if Kentucky had become part of the Confederacy (either through secession or by conquest), then the Confederacy would have been unconquerable.
Besides the additional population, the fact is that border states were more industrialized than the lower south was. Louisville would have been the second largest Confederate city, second only to New Orleans, and would have put the sixth largest Federal city, Cincinnati on the border. Also with a Confederate Kentucky, the Confederates could have built better defenses for the Tennessee and Cumberland Rivers than they did, and have been better able to prevent West Virginia from forming. Lastly, the defense of the Confederate middle would have been much easier to achieve if the Ohio River was the border. If Kentucky had seceded in April 1861 after Fort Sumter fell, I don't see how the Confederacy is defeated soon enough to allow for Lincoln's reelection in 1864.
Second, can anyone devise a realistic (as in not ridiculous) scenario by which the Confederacy undertakes a successful conquest of Kentucky?
You'd need to somehow drive Kentucky into the Confederate camp for real instead of the semi-secession that happened, and have it happen fairly early in the war. Maybe have Fremont (or someone of similar temperament and ability) instead of McClellan be assigned to head the Department of the Ohio in May 1861.