WWH explained it pretty well. You only have to make the brain bounce against the skull, with enough force he'll be knocked out, and Midnighter can definitely put out that force, Cap might as well, he did take down Hank Pym at full size after all.
Consider though that if Bane lands the first hit (his venom amped strength is like Class 1 but with a Addy skeleton it'd be up to Class 5 or even class 10, not sure what the multiplier factor is) Midnighter is paste.
__________________
“Where the longleaf pines are whispering
to him who loved them so.
Where the faint murmurs now dwindling
echo o’er tide and shore."
-A Grave Epitaph in Santa Rosa County, Florida; I wish I could remember the man's name.
Well no, Wolverine is around Class 2, and the Adamantium doesn't increase your lifting strength, it just adds something like a weight behind your punch. Bane would be Class 2 at the highest, and Midnighter is too much for him regardless, he's taken down Apollo, Seth the 6 Billion Dollar Bastard, etc... People way faster and stronger than Bane.
How did he manage to take down Apollo? Was it a really cloudy day?
Edit: at the very least the adamantium will allow him to punch guys like Spider-Man and not hurt himself.
__________________
“Where the longleaf pines are whispering
to him who loved them so.
Where the faint murmurs now dwindling
echo o’er tide and shore."
-A Grave Epitaph in Santa Rosa County, Florida; I wish I could remember the man's name.
A normal person can punch Spidey and not get hurt, his skin is durable, but it's just against blunt force trauma, it still feels like skin. Now if you hit somebody like Thing or Colossus, then you'd be feeling it.
He moved faster than Apollo could react to, and he used his staff to pop his ear drums.