The only problems I see with Carlos'n Charlie's
 is that I'd think it should be Carlos 'n' Charlie's. If Carlos and Charlie had each their own restaurant they would be Carlos's 'n' Charlie's Restaurants, but if they jointly own one restaurant then the apostrophes in the original are correct insofar as the possessives go. If you are using the other apostrophe to indicate the missing a in and[/], then there should be one for the missing [i]d, too.

As far as the examples given in the lovely AnnaS's link, I'm not so sure that the one in the pizzeria's name is wrong.