Pelvic tilts: Laying on your back with knees bent - rock your pelvis back - flattening your back against the bed and return to neutral, and if it doesn’t bother you progress to arching your back a small amount. Oscillate back and forth.
Knee to chest: Bring one knee up to your chest, stretching your hip and your back. You can progress to both knees to your chest.
Trunk rotation: Laying on your back with knees bent and together slowly let your knees go to one side - allowing your trunk to rotate. Switch to the other side. If that does not bother you, you can progress to have one leg straight and let the other knee hook over it - allowing the spine to rotate more. There should be a slow stretch in your spine.
Cat / Camels: On you hand and knees - you can arch your low back up and down. Focus on a slow stretch trying to move from your lower back and pelvis. Many times people arch their backs but move mostly from the mid-back or thoracic spine, which does not stretch the lower back as well.
More importantly - back stiffness every morning indicates that your mechanics are not working correctly. Usually morning stiffness indicates that the day’s before activities were too much for your spine to handle. Like working out for the first time - your muscles are sore the next day. This could mean that your sitting or standing postures at work are incorrect, to the way you walk or exercise puts too much stress on your back. There are many treatments to help address your back stiffness. At the practice I work at - we focus on manual therapy to help improve the lumbar vertebra movement and its surrounding tissues or intramuscular manual therapy (formerly known as trigger point dry needling) to treat muscle or fascial restrictions in the spine in such muscles as the multifidus, quadratus lumborum, or psoas. We also prescribe proper exercise progressions to stabilize your trunk and hips, as well as assess your movement patterns and postures in your daily activities. By improving the movement and stability at your back many times patients feel less morning stiffness as the area has better mobility.