We once had a big buildup of hard-water deposits in one toilet that was seldom used, and plumber strongly recommended against using some of the harsh products on the market (such as CLR, a popular cleaner which stands for Calcium Lime, Rust).
Instead, he advised bailing water out of the toilet and letting vinegar soak in for a while.
Don't know how well that would work for your particular stains, but a web search shows a variety of products which might work.
against rust, etc.
For routine cleaning and gentle but somewhat tough scrubbing of toilets, I really like the Clorox wands that come in a package with little bleach-containing scrubbers, which attach to the wand and can be thrown out after use. So simple to use.
I don't think using Coca-Cola sounds weird as a solution, either. That drink contains a lot of phosphoric acid that can even dissolve teeth if you put teeth in a jar of Coke and let them sit for a while. Probably works great on stains!