If you are ready for more challenging core exercises, here are some ideas.
Quadruped (hands and knees): Once you can do arm lifts and leg lifts with good technique and long hold times, you are ready for opposite arm/leg lifts. Get onto your hand and knees. Find your neutral spine position, then draw in your abdominals. Lift one arm and the opposite leg and hold for 5, 10 or up to 30 seconds. There should be no movement in your spine as you hold the arm/leg lift and as you lift and lower the arm/leg. Also, do not lift your arm/legs any higher than your trunk (you do not want your back to extend but to remain neutral). Once you lower the R arm/L leg, then lift the L arm/R leg. Repeat with alternating lifts for a total of 1-2 minutes. To challenge your core, increase your hold times. Then you can do fewer reps.
Plank: This is even more challenging! Lie face-down on the floor, mat or firm bed. Lift your hips upward and push up onto your forearms and toes, to form a plank position. Be sure to find your neutral spine position (you do not want your back arched up or downward). Hold the position until the point of fatigue and then rest down onto the floor/surface. Try to hold for at least 5 seconds. Do not hold any longer than you can maintain the neutral spine position. Work up to longer hold times progressively by practicing for 1-2 minutes/day. Here is an example of how to progress. If you practice consistently, you should be able to hold for >30 seconds within a few weeks.
Day 1: 5 seconds x 5-10 reps
Day 2: 5 seconds x 10-15 reps
Day 3: 10 secons x 6 reps
Day 4: 10 seconds x 10 reps
Day 5: 15 seconds x 4 reps
Day 6: 15 seconds x 7 reps
If you really like core strengthening, I highly recommend Pilates! A DVD or class at the gym can get you started. Once you learn the positions, you can easily transition to doing them by yourself as part of your workouts.