DeadBug
This is a relatively low load core exercise and is usually well tolerated even in those who have back issues. Lie on your back with knees bent and feet flat and "set" your tummy muscles so that you keep your core nice and stable.
Then reach one arm up overhead and stretch the opposite leg out straight and then lift the arm and leg about 6" off the floor, while maintaining a neutral and stable spine. Bring the arm and leg back to the original position and repeat on the other side. Repeat as instructed by the coach. You can progress the difficulty by holding a light dumbbell in your hands, and using a flexible cuff weight strapped around your ankle. Weights of 1-5# would be reasonable. Start with no weights and don't progress to weighted until you're strong enough to do 20 reps with good form.