Alright this took more than a few tries even after playing the game for a year. Abyssinia is in a terrible diplomatic situation because of their heretical religion, and open war with the Fatamids is certain to go poorly for at least a hundred years. So I have come up with a few suggestions. Before starting the game send your chancellor to Cairo to impress the Caliph (My chancellors lived in Cairo until I became king of Arabia). Also marry into the Byzantine Empire, you may have to pay them but they will usually send at lease 10k soldiers if their opinion of you is over 50. (This may mean some expensive gifts but you cannot fend off the Fatamids without help. Also try to marry your heir to get an alliance with HRE, so that you can either pay the HRE or the Byzantines to help. Also increase crown authority and change the succession laws to elective.
Lastly, before you start the timer declare a holy war for Harer and make sure you have soldiers in all of their provinces because Axum will also declare a holy war and you need as much territory as possible.
Next I declared a de jure war on Nubia and then Axum. Grant 3 territories and a the duchy of harer to your heir (if you grant any more than three he will start giving provinces out to randos). At thus point the caliphs opinion of you will have dropped below 50 and you will have to spend the 300 plus to keep him from attacking you. Never have less than 600 on you in case the caliph does declare war you will need mercenaries and to bribe either the HRE or the Byzantines to join your war. At this point you are probably on your second king and make sure you betroth your heirs to geniuses so that you can elect an heir with a genius grandson. Eugenics is crucial to your survival. If you need to look up the ckII eugenics page. Try to give all of your newly obtained provinces to your family members as this will help your diplomatic relations with your vassals. Now either wait until your relations with the caliph exceed 75 or until the Fatamid s have a civil war and have a holy war for sanaa. I chose to keep several of these provinces in my demense because the could have four or five holdings. Always send your chaplain to convert the populace in your demense before sending him elsewhere. At this point make sure you are having many children so as to keep alliances with the HRE, the byzantine empire, and possibly France. If your wife stops getting pregnant, kill her and marry another genius. Next I took over Oman and much of the Sinai peninsula by waiting for the seljuks and Fatamid s to have civil wars and then claiming holy wars on their duchies. (The hashamids tend to rebel often during the 1200s and the duchy of medina is a very good one to hold so seize your opportunities) Good luck i hope this helps. It is 1200 and i am the emperor of Arabia and the Fatamids are almost nonexistent so it is possible just difficult. Let me know if you want more information because I am aware this is only a brief introduction. Good luck.