Strengthen your core. Increasting your core strength is essential to reducing stress across your back. Before any exercise think "belly button to spine" to stabilize the back and perform proper breathing as well. For instance, if you are on your back doing leg lifts do not let your back arch; keep contact between your back and your hand underneath. Keep any weights close to your body to avoid increased stress as well.
Lower body workout. Depends if you want aerobic or anaerobic. For the aerobic part, stationary bike or similar sitting/reclining device. Water aerobics also low stress. For the anaerobic part, any core program is great. Consider a low weight/high rep program (30 reps with a specific weight/exercise). Avoid any exercise that hyperextends the back (common when tired and lifting weights).