You would want to design and test a vectoring nuclear thermal rocket built to absorb neutrons and reduce thrust on one side, and burn 100% on the other side, with the ability to gimbal the thrust vector depending on the asteroid's orientation. This gives you a much bigger margin of error versus "white paint" or conventional rockets imo.
You probably wouldn't want to nuke it, because you risk buck shotting the earth with a cloud of asteroids. Having a vectored nuclear rocket also allows you to change your trajectory if your initial calculations are off.