Core strengthening occurs naturally within the yoga practice. However, I find that certain exercises can help you in gaining strength faster and allowing your practice to progress more. Forget boring ab exercises, these moves will get your heart pumping. Make sure your lower back is always in contact with the mat ;)
Starting in baddha konasana, on the inhale bring your hands over your head and on the exhale elevate your body by engaging your core and bring the hands forward.
Start by laying down on your mat. On your exhale bend your knees towards your chest and bring your triceps to touch your knees. Hands are parallel to the floor. You are also engaging the hamstrings (feet to glutes!).
Using the same arrangement that you do in garudasana (upper leg and lower arm from the same side), use the inhale to separate knees and elbows and on the exhale bring them together. Do both sides. Caution: these are harder than they look!
Keeping your lower back on the mat, bring your hands in front of you. On the inhale, lift up and on the exhale lower down creating small pulses. You can try to go all the way to 100 with these.