How disgusting! I am so sorry, I love coffee and has a very visceral reaction to this! I also had cockroaches when I lived in an apt bldg, and the extermination worked. I was lucky to have them only in cupboards and my garbage disposal (which of course I turned on). Since then, I have been terrified of having them come back. If you have them recurring so quickly in the coffee pot, I bet you have an infestation though, but just don't realize it.
I put boric acid around the floor in all my cupboards. Boric acid gets in the joints and somehow kills insects, I think it makes them suffocate. Sometimes it can be hard to find. I used to get it at these dime-store like places in the city, many run by immigrants, and it often looked like it was imported from third world countries The powder was white and not too obvious around the back of the cupboards and along baseboards and by all the cracks under the sink. Now I live in the suburbs and I think I found some at Home Depot but it was dyed light blue (American safety feature), which makes my kitchen look sloppier as the blue is much more obvious than the white powder. Boric acid only harms insects, not people, pets, although it probably wouldn't be good to eat too much of it, which I wouldn't put past a puppy.
If they are getting in the coffee pot via the cord hole, you might consider sticking steel wool in there. I have heard that steel wool is good for putting into little cracks and prevent rodents from getting in. If they are getting into your coffee pot though, they might even be just crawling up the side. I think it is the water that they are attracted to, but worms can eat coffee grounds, so maybe roaches can too. You might put your coffee pot on a tray and line the periphery of the tray with boric acid, although if you keep the coffee maker plugged in, they might just crawl down the cord to avoid the boric acid. Do not leave any unwashed dishes in the sink. I don't know if that means you might have to stop using your dishwasher for a while too, seems like they could crawl up some fittings to get in there and eat the food there too.
I would also recommend getting rid of any clutter. Roaches can hide in the tiniest spaces. I saw a roach hide in a fold in a paper bag once, unbelievable. I have heard they can come into the house in the folds of paper shopping bags and be shipped in boxes. When I had them, I bought plastic tubs with lids to put my under the sink cleaning supplies in and got rid of any secret little spaces they can hide. Then if I saw one under the sink, I could quickly pull out the tub and smash it before it escaped down the crack. After they were exterminated twice, I did not have a problem. If you are renting and your landlord is not addressing this problem, you may be entitled to withhold your rent until the problem is resolved.