As far as conquerors adopting religion, the only thing I can think of off the top of my head is the Ilkhanate. It was an offshoot of the mongols who conquered Persia and adopted Islam. Different offshoots of the Mongols might work well for this in general, if you don't mind them being too close to an existing civ. I could also, for an example, see a civ led by Kublai Khan with this ability (the mongols adopted Chinese culture almost whole-sale after conquering them).
My Civ suggestion is this:
The Gulf States
Leader: Zayed bin Sultan Al Nahyan
Capital: Dubai
UA: Rapid Development, Receive a 20% discount when purchasing in cities. After discovering flight, every purchased building provides +1 tourism.
UB: Ghaus, Harbor replacement; instead of the base +1 gold, the owner of the trade route receives +1 gold for every sea resource worked by the city.
UU: Corvette, Replaces battleship. Receives a %100 combat bonus when fighting in shallow water.
This civ is obviously very modern focused. The idea is pretty simple, but I think it leads to some interesting choices. You can either pay to steadily upgrade your cities throughout the game, or wait with fairly undeveloped cities to get a massive tourism boost from buying cheap older buildings later in the game. The UU is pretty useless coming so late in the game, but I wanted a late game UU and a naval UU to give the civ the right feel. City list would be pulled from UAE, Qatar, Kuwait and Bahrain, so that is why it isn't called UAE.