He should have sent in the military to break up the southern rebellion immediately as recommended by former President Fillmore, if he wanted a "take-charge" attitude. Also, supported Bell or Douglas over Breckenridge in 1860, and enacted some civil liberties laws.
The military had a high proportion of Southerners in its officer corps, was largely stationed out west and was not particularly large. Heck if Governor Pickens had not been an penny-pinching idiot, Major Anderson would never been able to make it from indefensible Fort Moultrie to Fort Sumter, and that would have left no obvious place for flashpoint early in the Lincoln administration.
If anything, aggressive action by Buchanan after the lower south started to secede would have only gotten the Civil War started sooner, and with the North in worse shape. It would have been entirely possible that Maryland, Kentucky, and Missouri would have gone out in early 1861, and that there would have been serious fighting in California as well.
Now there are things Buchanan could and should have done before the election of 1860, but it is hard to see how he could have done better after the election, and very easy to see how he could have made it worse.