Here's an example of a shaker tape seat done in one color. Shaker tape can be done on any chair that could take a fiber or natural rush seat as well, but I do not recommend it. The tape is cloth; and as such is much more susceptible to staining, and the color(s) fade substantially. Also, the more it is sat upon, the material stretches and begins to sag; making for a very uncomfortable perch. The "tape" comes in a couple different widths and several colors, and I require you to purchase the material needed yourselves (I can give you a couple names of suppliers).
My price for shaker tape starts at $95.00 for an average sized seat, depending on the size of the tape (smaller tape=more time), the size of the seat, and whether or not the chair has arms and/or rockers that impede the process.
As with all types seat replacement, there is a fee for removal of old material.