I finally beat this w/ Egypt on Deity, historical. After many tries, this seemed the optimum strategy:
First, starting position. Go east and a bit south to the coast. Having a coastal city for the last monument you will get is incredibly important. The Med. Coastline to the north is far too short of production to ensure you can knock it out in a reasonable amount of time after unlocking it. I finally had a start with a marble hill on the coast. That was optimal. Don't waste your time with sub-prime starts. You'll never get the pyramids, even if you snag oracle. I'll say take a silver/gold on the coast, but only if marble is nearby.
After many attempts at using a marble on the hills one away from the coast, I realized my best production city, my capital, did not permit me to build coastal monuments. I made several attempt at building it from a second city on the Med. shore and other attempts from the shore to the south of the starting point, but the northern city will never have adequate production for monuments. The southern coast approach is far superior: you have far more production in that city available, usually including gold/silver/marble in the hills. Still, that city will be unlikely to be up to anything near as good as finishing the Great light house.
Do not bother with scouts. Monument then Oracle. It's OK to build Oracle while city is still at 1 w/ max production. Use your warrior to circle the map.
After oracle you have some turns to kick out a few units to find the rest of the Africa ruins. You can afford to delay because the other civs take some time to get more than a single scout down there. Don't open borders (although I think i traded the very first offer for 50g, so that the it would end by the time it mattered).
Order of Culture purchases: Tradition, Aristocracy, Honor, legalism, landed elite, Warrior Code, Military Tradition
build a worker between oracle and pyramids if you don't pick one up from the barbarians.
Build: Oracle, Pyramids, Zeus, and Lighthouse the second they become available on max production. All in your capital.
As soon as pyramids are complete, or soon as practical thereafter, build 1 settler to settle to the east of the mouth of the nile. Landed Elite and a granary are going to provide plenty of food while you run your city on max prod. with plenty of mined hills around, so kick out some archers then war chariots, with one or two spearman (if you are lucky, you will have your original warrior upgraded to spearman with two levels added after a big circle across africa).
From that city, launch an assault on the city state. Do not bother trying to take it. You just want to build experience to unlock zeus and great lighthouse. Once my second great general popped, my first one built a citadel one space away from the city state. Rotate your guys around to keep them alive at all costs. I had about 4 archers, three chariots, and one spearman, in between my city and the city state.
I had a granary, stoneworks, and a barracks plus the monuments in my capital (and a library, but that came pretty late.)
The other civs are unlikely to attack you before you make the turn toward the city state, which is the same direction they are coming from anyway. They seem less likely to DOW you once you DOW the city state, but that is pure speculation on my part, but based on my experience through several approaches trying to befriend or attack that city.
I've been able to get both oracle and pyramids on several different approaches, but this limited military endgame is the only one that got me the 4th monument. I'm not sure how people are claiming to be taking the other civs monuments (with Egypt), but i've never favored military approaches in civ, so i recognize that isn't my specialty. It seems to me the other civs' monument cities are simply too far away to get to with a sufficiently upgraded and balanced force.
Hope this is helpful to someone as frustrated with this as I was. This and Deity Khan have been the most challenging for me.
