Another of your ideas ...
This description sounds a little lame.
"The scientists believe it could be diverted by knocking material off its surface until it falls into a gentle orbit close to Earth."
My idea was to soft-land a mass driver. The momentum of multiple shots of small masses would slowly change the direction of the asteroid, and even large bodies could be redirected to safer orbits.
It only requires a robot with a small nuclear power source to power it.
It's "The Little Steam-Shovel That Could."