Okay.. I'll quote from a Friend (and main tester):
"I presume you mean how to get the one and only Rouge sex scene hidden in the game. A number of criteria must be met and a bit of luck. If you have missed getting a chaos emerald there is a chance Rouge or Shadow will appear in the street to offer you a chance to get an emerald from day 11 onwards.
They offer you a chance to get an emerald in return for cash and answering a question. Refuse to do it with “No chance” and there is a 25% chance of the game saying they stole an emerald and the back alley opening (leave and return to street and the new location can be clicked). There, they offer the chance to buy the emerald they stole back for £1000.00 or have sex in return for £500.00.
It's not all that easy to see as you need to be lucky to get Rouge and not Shadow to appear and then when Rouge does appear and you refuse her offer with “No chance” you only have a 25% chance of the chance of the back alley opening to allow possibility of sex with her. If you really want to see it, the easiest way is to get just one emerald on day 10 so there is something to steal, make sure you have £500 to pay Rouge, advance time to day 21 so that you missed the emerald on day 20, save. Then keep going to the street and if you meet Rouge tell her “No chance” and hope for the 25% chance of her saying “Oh NO! Rouge has taken one of your Emeralds!”.
If you get Shadow or she doesn't steal the emerald close the game, reopen the game, load and try again until you succeed. As the odds of Rouge/Shadow appearing when you visit the street are only 5%, Rouge appearing rather than Shadow are 50% and the odds of her stealing it are only 25% might take a while but I just tried it and managed it, so I can confirm it is possible."
Hope that helps ^_^