To build illegal shops you need to own businesses first....I bought a Hotel and it gave me an option to set up an illegal business behind the hotel...I put in a card shop but you have options of whore houses and such.
what u do, is buy a business then in the middle square, middle of the building it will turn blue which means u can buy, so u buy it then go into the menu and set up the business u want....and it has to be a building with business all around....just buy the business, then look for the middle to turn blue