coats of paint

depends upon what you're using for paint.

you might go with a primer base, tinted to 50% of your eventual eventual color, followed by a coat of good paint.

my guess is you won't know until you get 2 coats up.

The better paints have more hiding power due to higher pigment content.

I used behr paint with primer, one coat. I had to be careful to look for spots that didn't cover. Your colors, probably 2 coats. I painted my kitchen red, at least 4 coats using the old glidden without primer. Red over white.

Greg

You need a high hide paint. A bit of raw umber and black added to a white makes for a pretty good hide.

If you want to be safe and not have to worry about the number of coats of paint, you might consider a single coat of a white primer first and then the paint. I like to think of it as creating a white canvas for my topcoat of paint. I like using BIN but there are water based alternatives.

Good Luck.