Since you have already ruled that this is an impossibility in your campaign, my answer may be redundant, but I wanted to provide a counter point to the above answer of it being allowed; to show why it might be argued as disallowed.  (Also because @Miniman encouraged me to challenge his answer.)

[Here][1] is a link to a former question dealing directly with 'Divine Smite' being considered 'extra damage' for the purposes of burst/nova damage as some are calling it.


  [1]: http://rpg.stackexchange.com/questions/57077/what-is-the-maximum-damage-done-by-divine-smite

The relevant description from Divine Smite is as follows:

> "...to deal radiant damage to the target, **in addition to** the weapon's damage. **The extra damage is** 2d8 + 1d8 per Spell Slot level above 1, to a maximum of 5d8.

Divine Smite, and it's utilization of a spell slot to pull magical energy from to cause, very suddenly, the radiant damage to burst in addition to the weapon damage is what I believe makes it an impossibility to knock someone out with it.  That would be saying I could throw on Searing Smite , hit someone with my Warhammer which drops them to 1hp and then when the 1d6 fire damage explodes from my weapon as a result of Searing Smite, dealing it's full damage and potentially outright slaying a creature with only 4 max HP for example; I say I only wanted to knock it unconscious.

I don't have that option (as far as I'm aware).  Searing Smite would deal it's full 1d6 damage regardless of my intentions.  If I wanted to knock a creature out and my first attack only took them 1, I'd have to swing again, or wait until I could, and be cautious not to kill it with anything other than a melee attack.