I was actually discussing it on chat earlier
Current idea:
Point of divergence: circa 509 BCE, instead of replacing Tarquinius Superbus with a republic, they overthrow him and replace him with a purely Roman king. This Roman line develops, with the state religion becoming based upon Romulus as the king of the gods, with parallels to Hellenistic gods developing (names may be straight Roman with Quirunus instead of Jupiter, or I might mix things up a bit; this religion is known as Quirinianism, or the Quirinian Cult). The monarchy becomes heavily entrenched in Roman tradition, and is either never replaced by a republic or is only overthrown due to another Lucretia-esque episode 500 years+ down the line. I'm not 100% sure how the land will develop, but a Rutulian state countering Rome to the north could be interesting. As for an Islamic influence...we'll see

Suggestions are welcome.