Cockroach chao are among the easiest chao to get. There are actually two ways to get one. Here they are:

Normal cockroach chao:

Step 1: Get an Onyx chao from the GBA and hatch it (it's pretty expensive, so you might want to find someone who already has one. Tell them to mate their onyx chao with a normal one to get a baby onyx chao for you).

Step 2: Go find lots of dragons. A really good stage that lets you get two dragons in about a minute is Wild Canyon, played with Knuckles. Find the three chao boxes (one on one of the four ledges surrounding the "wind", and one in each direction from the center of the "wind", both left and right. Head toward the center of the stage when you first start and fly upward, then go both left and right to find two chao boxes. They're not hard to spot). Then go with Knux to the place you found his mystic melody in. If you don't know where this is, then climb up the wall at the END of each point of the two divided sections in the top of this stage. You'll see a painting. Dig into it and you'll drop down. Climb up the left-hand corner of the wall to find the second dragon.

Step 3: Bring your collection of dragons to chao world. Let your chao play with one dragon at a time until it gets antennae. If you get wings, feet, or paws, you'll have to go find skeleton dogs to delete those parts. You can find one of top of church mountain in Knuckles' Pumpkin Hill stage. Keep alternating between dragons/skeleton dogs until your chao will only remain with the antennae.

Step 4: Raise it as whatever type of chao you want, and keep feeding it to get its stamina high enough to let it metamorphosize. Spend time with it, too.

Extra: Don't let your chao get leveled up in its run stats. Let it continue to crawl, therefore making it really look like a cockroach!

Dark Cockroach Chao:

Step 1: Get a black egg from the market, or get a friend to mate their black chao with another chao to get a baby black chao for you.

Step 2: Give it antennae by following the steps 2-4 above.

Extra: I think this chao really looks cool. You can even get a collection of different-colored cockroach chao! Why don't you try a shiny black chao...?