If you have 100 years to work with, you may be able to use even simplier techniques such as solar sails or even dust to deflect the body (discussed here). However, if the asteroid is spinning as they tend to do, deflection via nuclear propulsion, solar sails, or many other techniques becomes a lot more challenging. In that case, using a penetrating nuclear weapon to blast off debris (imparting the delta-v) might be a better option.

A lot depends on the asteroid's composition. Some asteroids are really clumps of debris held together with weak gravitational attraction. A few years ago, some researchers ran simulations that showed nuclear weapons would be ineffective against that type of asteroid. Their simulations showed that explosion would cause the debris to fly apart but that the gravitational attraction would pull the pieces back together. Nuclear propulsion probably wouldn't work on that type of asteroid, either.