The method by which carabiners in any color are coated (either gate or body) is anodizing, which is going to be nearly impossible to sufficiently replicate with anything practical and cost-effective at home. With anodizing, the coating essentially becomes part of the aluminum itself. So anything you put on the gate will wear off relatively quickly and potentially cause the screw-gate to jam up. Nothing you paint on a carabiner or its gate will be permanent. Even the anodizing eventually wears off, unless of course you never use them.
Don't use the "metal markers", aka paint pens. The coat of paint they apply would definitely be too thick for a carabiner gate, and while quite tough, it's also less durable than fingernail polish.
That said, fingernail polish, as others have mentioned, is worth a shot. Carefully put a very light, thin coat on only the gate itself and not any crevices or threads. Before you apply it, make sure you clean everything well so the polish adheres with a green Scotch-brite pad, or similar pad (not the non-scratch kind). Aluminum oxidizes over time and will prevent the fingernail polish from sticking, so if you don't clean it, the polish will flake/rub off rather quickly for sure.
Whatever you do, do a test on just one carabiner first to make sure that the marking has adhered and also that the gate still functions as intended.
For what it's worth, I've never known anyone that has painted/marked the gates of carabiners. Spines are usually where any markings or taping end up. So any community standard that exists would be for identification purposes, either to determine ownership or if a piece has been retired to non-critical purposes (doesn't need to keep you alive).
Here is an example of even hard anodizing wearing off. You can't see it so much in this photo, but the under/inner side is even more worn than the outside.
