In reply to mypyrex:
A friend of mine suggested this, and i thought it was genius!!
You give them both a Big Red Button.
Say that when you press the Big Red Button, you deliver an electric shock direct to the other guy. Say it is all science-ish, and that they are the first leader ever to have done this. In fact, say that it was in fact their idea.
Then, at random times, the button gives them an electric shock, but you say that is the other one getting their own back.
The two of them could then spend days frantically jabbing at buttons, giving themselves electric shocks....