Al Qaluza
Reposting my Map of the Month entry:
In the early 1600s, the Kingdom of Morocco does a good job consolidating its authority. Due to butterflies, the 30 years war is delayed until 1675 (and is 26 years long). Morocco joins with France, and is able to take Granada and Andalucia (France takes Catalonia, and sends a Bourbon to sit on the throne of the rest of Spain). The Hapsburg Spanish flee to the Americas. The Moroccans follow, in an attempt to create their own colonial empire. They only just manage get a lost colony of their own established, before it is taken from them (Morocco sides with Bourbon France in the equivalent of the 7 years war, and France still loses).
Al Qaluza, as it comes to be called (the name comes from this:
http://en.wikipedia.org/wiki/Calusa#Name) , is turned into a sort of British protectorate. The British don't really want to absorb those Arabs, and so the local sultan rules. As the 'Columbian' Revolution breaks out in 1799, the Sultanate is overrun by the rebels. It becomes part of the Union of Columbian Republics (even more decentralized than the OTL U.S.). But Al Qaluza is home still to many Muslims, British Sympathizers, and Hostile Native Tribes (who've mostly converted to some form of Islam).
So in 1849, after much debate, Al Qaluza is allowed to peacefully leave the Union. But, per its independence agreement, it can never have a Sultan again, and must be a republic. Today, Al Qaluza (or simply 'Qaluza', as many Non-Arabs call it) is a vibrant two-party democracy, with over 80% of its population in Muslim. Immigration was slow at first, so Natives make up slightly more of the population than OTL Florida. Many people from the Middle-East (escaping modern violent dictatorships) have moved to the peaceful, rich, and neutral nation of Al Qaluza. There are also large numbers of blacks (more so than in OTL Florida) given that Al Qaluza was the last modern nation to abolish slavery (in 1890!!!). Its economy is closely intertwined with both New Spain and the UCR. These days, it is a bastion of Liberal Islam.