I've been thinking about this also.
Crayons and lacquer sticks wont last, even enamel paint will quickly dissolve away if you clean with RemOil or similar light solvent.
I've discovered that Xylene paint markers are the most permenant paint available for this task, that can easily be done at home. Many colors available. after a few months, my colored engravings are still holding-up fine, even when cleaning with RemOil.
I've got a video about it on my YouTube channel if you want to see how I did it:
Link for mobile: m.youtube.com/watch?v=EjGNm0HJV7w
This process uses Kroil as a solvent, so make sure you wipe off all the Kroil when done and re-oil with something gentler. I did this on several firearms now, a the main thing to watch out for is the rubbing process (to remove excess from around the engraving): rub too hard or too much may wear-thin some older (weaker) finishes (I have not had a problem, but just warning you).
But I've done this on several guns now, and so far so good...