even with minimal upper body strength, you can still work on just inversions on the rings. first in a tuck position, then extended legs, then a pike, then skin the cat, etc. also, try l-sits on the rings. you can modify by staying in a tuck in support, or extending one leg at a time.
as for ring dips Ė ive been able to work from zero to sets of 3 in about 6 months. keep working your negatives. once youre muscles are spent on those in a set, add one of those assistance bands. they can take 30 lbs+ off your weight, which should allow you to do sets with multiple reps. tailor workouts to have rings dips, and do them as negatives, assisted, etc.
you mentioned pull-ups: was this to indicate upper body strength? or are you doing these on the rings? getting pu's on rings doesnt translate well to the bar - learn puís on a bar. eva t has a great video on the crossfit site of how to learn the kipping pu. if you have good hip power and decent upper body strength, then you should be able to do them. i found two things helped me learn the hip power: doing some overhead soccer throw-ins and crossing your legs during the kip. sounds a bit odd, but helped me learn to fire the hip (once you have it, you can go back to frog kipping, etc.). same thing here, progression will be slow. i had zero kipping puís in jan (although could do several dead hang) and now have sets in the 15 range. until you get them, you can also work body rows.
[to qualify the response: im 6 ft tall, ~185 lbs, zero gymnastics background. im a remedial gymnast, but improving (albeit, slowly)]