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Unlike other options that require the precise application of small forces, nuclear explosions would require minimal detailed information about the asteroid while still being effective. This results in a simpler mission design that would only need basic details about the physical characteristics of the asteroid and its trajectory. The mission could also be designed to incrementally deflect the asteroid over multiple blasts which would reduce the overall technical risk of the mission. NASA has already designed the mission and spacecraft required to deflect an asteroid via nuclear explosions. See More
In a 2007 report to congress NASA found that the use of nuclear standoff explosions were 10-100 times more effective then any other alternative considered in the study. The primary benefit of this approach is the amount of force it exerts on the asteroid. Unlike other techniques that require years to work, this approach would be effective on asteroids mere months away from impact. This is critically important as our goal for 2020 is to be able to detect 90% of the near earth asteroids. Our current capacities are well below this, and even when implemented the new systems will result in a significant portion of the asteroids remaining undetected. This number increases dramatically if 20-30 years notice is required for the deflection of the asteroid, making the ability to quickly react to an incoming asteroid critical to our survival. See More
Significant amounts of technology testing would be required for this method to be validated in effectiveness. For instance, the surface properties of the asteroid must be taken into account: A dusty surface combined with the impact of the paintballs would reduce the surface % covered by the paint. Microgravity (assuming the asteroid mass is small) would inhibit the effectiveness of the paint contact to the surface - reducing the surface % covered by the paint. See More