Depending on your budget, you may be able to find fabric with a pattern like that already on it. For instance, I've seen lace that is essentially black circles on black mesh; layering that over a solid fabric could give you the look you want. Alternatively, this site
allows you to basically design your own fabric; you upload an image, they repeat it all over the fabric and send it to you. Look around and see what you can find before resigning yourself to handpainting everything.