There is an entire science to your question, called "anti" workouts. The main goal of the core is to resist tension, not flex or bend, which is why your back might hurt. If done correctly, this shouldnt put ANY pressure on your back(if it is you arent doing it right).
Resisting extension, vertical pallov press, ab wheel rollout, deadbug
side plank, side pallov press, suitcase carry/deadlift, one armed farmers walk
landmine twist, pallov press, one armed dumbbell bench
plank, ab wheel rollout(use a barbell to add resistance), hollow hold, deadbug, zercher squat hold(hold barbell in crooks of arms standing up for 10 seconds)
off-weighted exercises(doing a dumbbell shoulder press with one arm, dumbbell bench press, or deadlift with weight on one end).Off weighted exercises work the core great. you can make a bigger weight difference between the two sides to increase ab tension.
All of the above can have weight added to them with exception of side plank. For one
These are all exercises to resist actually bending. mix a fair amount of isometric and dynamic versions(holding a pallov press for 30 seconds, versus doing 15 reps for example).
Also if your back is hurting, even during regular ab exercises, you probably have very bad form and need to check your pelvic floor/posterior tilt, etc.. there is enough to write 20 to 30 pages here, but you really need to research this and possibly get a fitness trainer/physical therapist to make sure you arent injuring yourself. that being said, all the anti exercises 100% wont hurt your back