Would you like to get a six (or eight) pack of abs without ever having to do a crunch or sit up again? I'd put money on it that it could be done by doing more training on the rings.
One of the great things about ring training is the instability (read "lack of stability") that they offer and how they make standard movements so much more difficult!
While some may see that as a reason to avoid the rings, I see that as an opportunity! The instability of the rings requires your core to be turned on 2x more than on the bar or floor.
The key to making your core work is ensuring you do QUALITY movement and squeeze your core throughout the FULL RANGE of every repetition.
You'll know you are doing it right if when you come off the set your core is as fatigued as your chest, shoulders or grip. In fact, try to squeeze and engage your core harder than every other muscle in the body.
Pro tip: Shorter sets, higher engagement
Kettlebell guru, Pavel Tsatsouline, is known as being one of the top strength coaches in the world. One of his secrets to building massive core strength is doing planks, where you hold your body either on elbows or hands (similar to the top of a push up position) and squeeze as hard as you can for only a few seconds before taking a rest. His theory is different than traditional planking theory where you hold the position for upwards of a minute or longer. The shorter duration holds with higher intensity delivers more outstanding results because you are getting much higher muscle activation.
I believe 100% in Pavel's theory and have seen the results in my own training.
On the rings and in every drill you do, squeeze your core like your life depends on it, and keep the reps lower and quality higher. The results will be immediate.