I don't think such a partnership is possible, at least not in the way you imagine it. Why? Because of money. I'm sure Sony would want some of Nintendo's handheld profites, and I don't think Nintendo is willing to share those. If they made the HW together, that would mean Sony gets some of all the license fees from that handheld, and it's quite obvious that the 3DS is doing fine without Sony. I'm not sure how a phone would work though.
As for home consoles, I don't think Nintendo is willing to give up their right to make any HW they want, which means that they would have to co-develop the next consol with Sony. Which of course means that Nintendo would get some of the license fees from all 3rd parties publishing on that console. And why would Sony share? They don't need Nintendo to make money on that front.
What you've described is a pipe dream.
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Furthermore, I think VGChartz should add a "Like"-button.
