Board Games/Carrom board coins color.
what could be the alternative colors used for 9 White,9 Black and 1 Red Queen coins color in a carrom board?
Realistically... whatever you like. The White, Black and Red are chosen to be easily distinguishable at a glance. The core purpose of the colors of pieces is so that nobody gets confused understanding which colors belong to whom.
If you're going to substitute another set of pieces, my only recommendation is to make colors that are easily distinguished. Also, it's important to think about folks who may have color blind issues. For instance, I have a close friend who is red/green color blind, so if your set used colors like that, he wouldn't be able to tell the pieces of one player from the other.
If you're making your own set, go with whatever you like. A good recommendation is to look at sports teams colors as they're almost always very contrasting (For instance, in my home of Seattle, Dark Blue and Sea Green are the colors of the Seahawks and those colors contrast for just about anyone). If you're looking to make a set to sell commercially, take a look on the web for sites that assist in color contrast. The most common type of color blindness is Red/Green, so be careful of that. If you're concerned about something you're trying to sell on the open market, consider symbols on the pieces that allow a color blind individual to tell the difference. A Star on the red pieces and a Circle on the green pieces would allow anyone to tell the difference visually.
In your case, you're also talking about a third piece... the queen. With that, just make sure it's EASILY distinguishable. If your colors are going to be Dark Blue and Bright Orange, don't make the queen piece Red since the orange and red might be confused during the exciting heat of a game.
But, realistically, these suggestions are really up to your taste.
Additionally, I highly suggest testing whatever coloring you're going to use beforehand. Many Carrom pieces are lacquered to provide nice, smooth sliding across the board. If you decide to pain them with spraypaint, spraypaint has a tendency to put a bunch of small particulate matter on the piece and that may interfere with the nice smooth sliding. Unless you're going with a wood stain, whatever method you use for coloring is going to change how the pieces slide. Find a wooden dowel or something that you don't care about and run some tests with your paint. You'll be much happier discovering issues BEFORE you go painting all your pieces.
Hope this helps!