My solution was the DS/3DS line of consoles... snap 'em shut, bam, paused. I've called them the consoles of choice for the discriminating father.
(If you've never had kids and find yourself wondering what horrible father would be playing video games while taking care of his children, well, you see, it turns out that sometimes your child wants to sleep on somebody, and will not sleep any other way... and there's only so many things you can do with a baby that cries if you move sleeping on you. Both of my kids went through that phase for different reasons.)