I have 2 toilets where I had to deal with this. (Yellow / orange calcium rings at the waterline of the bowl). My wife tried all the cleaners. CLR, Lime Away, Rustoleum Rust Remover Spray, Mister Clean "Magic Eraser". Name it.
None worked with any satisfaction. So I tried a small Scotchbrite Pad, (Tan, dark Earth color). And some Lime Away to wet it with. 100% success! The calcium deposits were heavy, and raised up over the glazed surface of the bowl. You could feel them with your fingernail.
I used only one finger, pressing lightly directly over the ring, using back and forth cleaning strokes. It took a bit of doing, but all of the calcium stain rings vanished. And when I dragged my fingernail over the surface, I couldn't feel anything.
I washed and wiped the surface dry, and used a magnifying glass with a bright LED flashlight, and I couldn't see anywhere that I had scratched the ceramic glaze of the bowl itself. It really worked much better than I thought it would.