Funny you should ask... sadly, I'm away from my computer that can play CKII for the weekend, but I can speak from personal experience that survival as Nubia in 1.07 isn't only possible, but I've effectively done it, and without the aid of cheats or mods (yes, Shia can holy war/invade me as they please).
It's not easy, nor is any attempt, even knowing what you need to do, a guarantee. Early on, luck is a huge factor. But, this is what I did...
1. I started in 1076. Before then, the Caliphate is simply too powerful, and the amount of pure luck required is simply too high. If you start in 1076 or later, however, you're looking at a Caliphate that's down to mainly Egypt... they're still one of the most powerful forces in the game, but they can be deterred.
2. Restarting: you're gonna have to a few times. If the Caliphate comes for you at the start of the game, you're doomed. You'll lose 2/3's of your provinces, and then either Axum or one of the Caliph's vassals will come calling for Hayya. But they don't always come for you immediately: sometimes they'll target someone else first. But what you really need is...
3. For the Seljuks to declare war on the Caliphate. If they don't immediately implode, the Seljuks may very well declare a holy war for Sinai. It'll be lengthy, brutal, and the Caliphate stands a solid chance of failure.
4. Allies: Nubia doesn't have too much going for it, but one of its advantages is its status as a Kingdom and you've got a King and heir with no wives. From the get go, I managed to ally up with both the HRE and England. They're both going to complain about distance when you call them to war, so do whatever you can to make them love you; send your chancellor to improve relations, scrape together cash for gifts, offer children as wards, ect. If you're quick and lucky, you can declare your own holy war on the Fatimids while they're being slapped around by the Seljuks. If you're confident you'll have tons of help, feel free to head straight for Cairo... I could only convince I believe France to help with that first war, so I was safe and just snagged the county of Aswan. Even that, though, is a nice boost.
5. Be aggressive. You can't sit back and just wait for the Fatimids to burn out, or to hope for any kind of co-existence. So long as they're your neighbors and own Cairo, Alexandria, and Damietta, you're survival is in (dire) jeopardy. Those duchies are simply too rich (especially Cairo and Damietta) and bring in too much manpower to remain in their hands.
6. Don't forget Axum! Not only can they claim Hayya via de jureness, but if they fall to Abyssinia you could be in even bigger trouble. This is another point where I lucked out: I switched to elective monarchy, thus forcing me to land my son... and, as luck would have it,
he fabricated a claim on Axum. Abyssinia started to wail on them, so I dog-piled on and took much of the duchy for myself. Once you have the ducal title, snatch up the rest of de jure Axum from Abyssinia. It'll give you some easy boosts to your levy size, and it'll make Abyssinia weak enough to leave you alone. And if you're lucky, they'll go ahead and conquer Harer. Speaking of which...
7. Harer is a tricky choice of whether or not to take after you drop Axum. Its land, and thus money and men, but if Abyssinia takes it, it means you no longer have to deal with Muslims coming from the south for the time being. Despite how I handled it in 1.05 (where I gladly holy wared for it... and Abyssinia and Axum, when cause back then they were Monophysite and Nubia was Orthodox), I actually went the opposite route here. I ignored Harer and let Abyssinia take it, and let them go on to try and fight off Sanaa. Eventually the Hashimids of Mecca broke across the sea and took Harer which in turn forced me to finally go for it, but until then it wasn't my problem. I kept my men and my money in the north to fight the Fatimids.
8. Kind of a re-iteration of #5, but be opportunistic. Back in the day, one could just retreat into the desert and let the Fatimid forces die of thirst. Now, they'll just storm the crappy, poorly constructed walls of your crappy, poorly constructed castles and you'll be looking at "game over" long before their stacks wear down to a manageable size. And even if you do kill a few Fatimid infidels, they'll just call in the terrifying force of the Hashishin. Nubia can't win a straight fight with the Fatimids, at least not until they take two of three richer duchies from Egypt... and no, not even if you take all of de jure Abyssinia. There's just not enough men there alone to make a united, frontal attack on Egypt. Instead, wait for them to go elsewhere. Ever see any threads here about people raging because the Fatimids called a Jihad for Aragon or Galicia? Believe it or not, they don't call those only on the player. If they call an overseas Jihad (and they almost certainly will), get ready: butter up your allies, watch the movements of the Egyptian forces, and wait for them to get on their ships and sail away. When they do, declare your holy war for Cairo or Alexandria and call the ERE or HRE and whoever else you've got to help down to the desert to stomp them in the face.
9. Okay, this isn't super important, but taking Alexandria means you can vassalize your religious head! Once Alexandria is in the hands of Most Glorious Nubia, simply put any random courtier in charge of the Bishopric. The Coptic Pope
should replace him and proceed to be your vassal. Alternatively you could leave him unvassalized for usage of the Invasion CB, but meh... having what appears to be Ron Jeremy with a spray tan as a vassal is far cooler. The real advantage here is now you can excommunicate the sorry ass of any other Miaphysite you wish, though given how limited the religion is, its rather limited in power.
And eventually, it'll all start to look like this (and yeah, my only screenshot I've taken... and I've since claimed Damietta as well, and yeah, county is in revolt):
To summarize, the keys to Nubian excellence are: 1076, luck, allies, luck, being opportunistic and aggressive, and an absolute mess of luck. But once the Fatimids are effectively crushed, the possibilities open up (as they do with every game where you reach the point that complete failure would be a challenge). Do you press west and try to claim Africa from Busaso to Ghana? Do you invade Europe from the south, or perhaps strike from Harer up through Sanaa to claim Arabia? Or perhaps its time for the Miaphysites to claim the Pentarchy? I'm personally planning for the last one... though I plan to intentionally set up an independent Abyssinia with Gondar and Harer. But first, I gotta wait for Axum to de jure drift into Nubia.