Most every actual ship had black ratlines and standing rigging. Only the running rigging was a lighter color - usually tan or light brown. The reason standing rigging was black was because it was heavily tarred to prevent rot - not to mention failure at critical junctures. If you are building from a kit and weren't supplied with black rigging line you have a couple of options; 1) contact the manufacturer of your particular kit and request they send you the right line for your ship, or 2) go online and order rigging materials from someone like Model expo or other reputable dealer. If you are building from scratch it's a bit tougher as the rules for the size of rigging lines are pretty complex and you would have to do some math to figure out what size you need depending on the period of your ship. And if that's not confusing enough - it also depends on whether the ship was built in England, France, Spain or Holland. The US usually followed British practices.
I have used a spirit based ebony wood stain on rigging cord. Just immerse then hang up to dry.
Indian ink! ( The real stuff, not fake) Works like a charm . Keith Juleir recommends in his books. I painted it on after rigging an it makes all the rope the same shade as well as the waxing & glue marks. Does not damage cord.
I run tan line under the tip of a permanent black marker. Heavy line might require two passes but works for me. For smallish line I buy black sewing thread.