You can shoot without a tripod, however I wouldn't recommend any auto modes... Shoot in manual or aperture priority with the following settings: f2.8-f5.6 max. ISO 800-1200, and your exposure value should be between 0 and -1.
Use a wide stance, and hold the camera and the end of the lens. Anything you can brace yourself against will help.
Try to shoot corals that are perpendicular to the camera... shooting top down works very well for this reason. Your focal plane at this f stop without a tripod is going to be very narrow.
Good luck!