Try the baking soda. I have a liner pool and that is what I use. You know the kitchen sponges that have a sponge on one side and the other side is a little rougher? (Not TOO rough, though.) I put some baking soda on it and gently rub the waterline. Having said that, my pool doesn't have the oily ring that it seems yours does because we mostly swim in the evenings so sunscreen isn't needed. But, it won't hurt to try the baking soda and won't hurt the chemistry as long as you don't use buckets of it!