Una cucaracha pinta
 

le dice a una colorada...

I tried everything, including the RAE dictionary. Pinta as an adjective is either nonexistent or irrelevant. Judía pinta certainly exists, but its etymology is uncertain.

Meanwhile, the context suggests some kind of appearance... And after all, the song hasn't been created by eggheads. Must be something familiar to any Mexican, at least. What is it?

Pinto beans are tawny in color when cooked. Fresh out of the pod, they are white with reddish spots. I have never seen a spotted roach, but there are plenty that are light brown, a color close to cooked pinto beans. Perhaps cucaracha pinta is a term used to distinguish them from blackish roaches. I'm not sure if the variance in the color indicates subspecies or a phase a roach's life.

"Pinta" means "spotted" and "colorada" means "red".
Since the popular song is some sort of fable, there can be cockroaches in different colors. ;)