Food Coloring for Rubber-Stamping

I have never tried using stamps, but when I have painted cookies that refuse to dry completely I dab them with powdered sugar and a round brush. Just dab up and down (not side to side) once the paint is dry enough to feel tacky, and then brush off the excess. The color will be slightly more muted, but it seems to set the dye.

When I took a class from Arty she showed us painting.  She said found that painting worked best with Wilton.  Maybe the same is true with stamps.  I’ve never been successful with stamps.

I stamp with liqua-gel food coloring. The key is not to apply it too heavily. (It looks like it's pretty heavy in your photo.) To ensure a light, yet uniform coat, I just moisten an uninked stamp pad with the coloring, and blot off any excess before inking the stamp. I find that the coloring dries quite quickly this way, regardless of the brand used. (I have used many types of liqua-gels and gels, but I most often work with Chefmaster.)

Airbrush coloring, especially if alcohol-based, will dry faster, but I don't use it because I find the coloring too loose, making the stamp more prone to sliding around while stamping. But some people seem to like this approach - most seem to airbrush it directly onto the stamp.

Thank you everyone for your help!

As a troubleshooting, I tried the Aproned Artist method, except that I used cornstarch instead of powdered sugar in fear that it would just make them more tacky. Seems that it solved the problem, but next time I will try the suggestions of Julia as well. Thanks again!