How fast would a planet have to be travelling to appear overnight

Bikenbeer has it correct.

Morning fox has not even noticed that his speed is greater than the speed of light.

fox new is crap, and as far as planets moving that fast.. well anything is possible, hell we still don't know why hot water freezes faster then cold... just saying ... i like turtles

About 60 million Mph ( that's 16,666 Mps)... Even then it still may need to be traveling a little faster.

If it's part of the solar system (and the doomsday loonies talk about a predicted return, so must apply to their planet) then it has to obey the speed limits set by the gravitational pull of the Sun. In the vicinty of the Earth, that would limit it to 42 km/sec (escape velocity from the solar system). A Mars size object would therefore have to have been visible to the naked eye for more than a year. Extend this to several years if you include telescopic observations.
So nothing large is going to suddenly pop into view on 21st December, having previously been undetected.

I figure it would have to be going at least 350,000 km/second. That's more than 8000 times faster than the Earth goes around the sun, and about 1600 times faster than the sun goes around the galaxy. Now, it might not be too extreme to imagine a planet moving at 3,500 km/second. But 350,000 km/s just doesn't seem at all within the realm of fact-based reality.

By the way, 350,000 km/s = 783 MILLION mph

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Ha, someone noticed that 350,000 km/s is faster than light speed. Yes, that's right -- Nibiru would hit us before we saw the light! Because any lower speed would mean that astronomers would have see it many years ago.