There are 2 main types of air-dry clays....those that are pre-colored and those that are not. Most of the clays that are not pre-colored are white or off-white in color. (A few are terra cotta or gray.) The question of what to use to pre-tint the "white-only" clays comes up quite often (the alternative is to paint after cured).
The answer is: Just about anything soluble!
You can use paints...craft paints, artist acrylics, or oils paints. You can use cake colorants (not food coloring) that are made in paste and gel form and also the 'pearl dust'. Artist pastels, crushed into a powder and mixed into the clay will make soft, pastel colors. You can also use the inks and chalks popular for scrapbooking and rubber stamping. There are also colorants available that are specially made for tinting air-dry clay and cold porcelain, but these don't seem to be readily available in USA (yet).
Mixi at Kawaii Frenzy has done some in depth experimenting with colorants using inks, acrylics and oils. Mixi was testing the tints using Lumina Clay* however, her tips would apply to many other air-dry clays. Click here to read her results of coloring Lumina clay and what works and what doesn't.
*Lumina clay is waterproof, translucent, highly flexible, durable, acid free and non toxic. Please check the LABELS in sidebar for more posts about Lumina.