Making a Cannondale BadBoy ride softer
Wider tires are the first thing to try. The BadBoys are basically rigid mountain bikes with 622mm wheels and narrow tires, so you could also put on mountain bike sized wheels and very wide tires. With a second set of wheels, it's easy to change between road and off-road riding.

About suspension forks, with current geometry there isn't much room for the suspension to work. You could install a 29" suspension fork, but that would change the bike's geometry.