I've seen a lot of discussion about color in zentangle/zendoodling and worries about it overpowering the zen or causing too much thought which might pop the person out of the 'zen' mode.
So-o-o I came up with a pattern designed to help you use very subtle coloring. I'm using lines, because it helps you keep the color softer, but you could use a scumbling effect (using the side of a pencil lightly). The other advantage of line is that you can easily use colored pens, versus pencils or pastels.
The idea to keep in mind is blue shadows on snow--atmostpheric, soft, beautiful. This was supposedly the inspiratation for impressionism, and this method borrows heavily from that discipline.
The first tip--how to avoid thought? That's fairly simple. Choose your colors before you start. Alternate them, and apply more color toward the bottom of the fluffball.
The second tip--use a paper that is rough. Watercolor paper is a good choice. You'll get a scumbling effect without even trying.
The third tip--don't press down hard and don't try to fill in solid color. Give your hand a rest, and let the paper do some of the work.