I've been playing Civilization for nearly 20 years, and only just beat a game on Deity difficulty. All hail Ghandigo, majority-elected supreme leader of the planet.
The trick is just to accept that you'll never be the best at anything, never even try to build any wonders, and only start building a proper military if someone settles on your doorstep. Focus on your finances, then just keep buying off the city states over the course of the game - AI factions on Deity gain a myriad of cheats, including lots of free money, but they prefer to spend it buying territory, units and buildings.