Black is just a human dude without his powers up and running, so it is conceivable that Joker could gas him in his sleep. But mind games against a global telepath seems like a losing battle.

I'm not actually sure why Joker would do that though-- Black's own personal brand of sardonic nihilism seems like something Joker would enjoy. A team up seems more likely, though I'm not sure Black is far gone enough to do that. Joker seems like a prime candidate for execution based on Black's original appearance. Black went on to team up with Lex Luthor and all, but that was while Luthor was president and ostensibly a good guy.