Arabia is a great civ for Autocracy (and also in general). Camel Archers will carry your midgame wars, and the double oil will ensure you can field plenty of bombers, battleships, and tanks. And the extra gold and lux from bazaars will help your self-sufficiency. Persia could also be fun for the Golden Age military bonuses stacking with Lightning Warfare and Clausewitz's Legacy. As Arachnofiend points out, Mobilization can be stacked with other cost reducers to make buying units dirt cheap; combine this with Total War, and you can have a large army of 3 promotion units very quickly. This can be an interesting option for any civ that gets a great UU that doesn't upgrade very well (Keshiks, Camel Archers, Winged Hussars, etc.) as you can quickly replace them with a fit fighting force once they're obsolete.
For Diplomacy, Sweden is an intriguing option (I'm about to start a game trying them with Autocracy). You can gift Great Generals/Admirals to Militant city-states to get them as allies, start a war to get faster unit gifts with United Front, and use your swelling army to leverage Gunboat Diplomacy while generating still more GG/GA with your wars to win over more city-states.
On the Culture side, as Arachnofiend says, mainly you just have to jump in wars with the right rival civs, but if you want to have some fun with it, go with Brazil for the aforementioned Pracinhas, Sweden again for the opportunity to generate more Generals/Admirals, or Aztecs to milk that culture bonus for all its worth. If you go that route, you'll probably want to refrain from conquering cities to avoid the warmonger penalty, which makes Ethiopia or India interesting possibilities.