Well the issue is that in D&D, a Paladin is a representation of the forces of good and law. What you're looking to deconstruct is the perception of Paladins or possibly the idea that people can be good, which is a far far worse thing. To have a Paladin (at least one in the traditional sense) be other than good is an attempt to deconstruct the very idea of good. Now there are worlds without morality, D&D is not one of them. A Paladin cannot by definition be amoral, therefore a deconstruction of a Paladin should represent the flaws in the idea of Paladin.
How you ask, well give the Paladin flaws, make him an alcoholic, or a deadbeat, or a somebody who likes to kill. Give him something to struggle against so that his morality means something. But to deconstruct the idea of good itself is a very difficult and philosophically involved principle. I personally would not play with somebody that tried to in essence break the game world in that way, and I am concerned that some of your players might feel the same way. Now you could have an LE antipaladin who still believed himself to be a paladin, or a CE antipaladin, who hid his chaos under a veneer so that he could get away with his vile and heinous crimes (after all chaotic evil isn't chaotic stupid anymore than lawful good is lawful stupid, and even CE people are capable of complex plains and ruses). But in game terms you cannot make someone good who is not.