Nah, King is just harder than Chieftain and warlord because you have no bonus attackig and defending, just try new strategies
you don't HAVE to win before 1000AD for example, you can win as well by being in a tech-lead in 2100AD (game forces end there)
Start placing your capital where you start, and put both working tiles on forests.
-3 turns later you have your first warrior to explore and get huts and barbs with, and 2 turns after that, your second warrior's ready to to the same in other directions.
Now make a choice :-Seen a lot of barbarians and huts you can get to? : make another warrior
-Haven't/already done the above? : put the 2 tiles on grass (2 food each)
I think you may have a problem teching fast and keeping the tech lead?
-Try using Japan, with them you get 1 food per sea-tile, so you don't have to worry about science and growth
And research these techs first: Alphabet, Writing, Code of Laws.
Accept the Republic government (Some people don't do this, I don't know why....) and make a settler from every city you have (I know that the first time you force yourselves to go settle can be hard, because your population decreases, and thus your science).
I think you will have 2 cities : your Capital and the free 100-gold settler.
So you'll make 2 extra settlers.
Put them at spots where you think is good for a settler, but don't forget to give them escorts; have a warrior in the same tile as your settler at all times for example (settler has 2 movement, but you can take 1 step and stop as well).
Then once you have your 4 cities, grow them to at least 3 population each, and make 1 settler in each of your cities, and you'll have a harder time finding good spots to settle, and that's the crucial part for beginners : Island settling!
you may have gained a galley from a barbarian village, so load in your settlers, and go to the islands around.
You'll have 8 cities once this is done, and quite a tech-lead.
But most important : you'll have tried making more cities and have found out the advantages of island cities.
of course you'll be able to work from this starting 'strategy' and perfect it for yourself.
In no-time King will have become to easy for you.
before I forget it; the defenses!
-Most starters forget making units untill they get attacked (and it is to late), so while you may want to get more science by settling near water, use at least one settler to make a city with lots of production (forests, hills, ...).
Make at least one archer army in each city (your certain of 2 forests near your capital, so thats 4 production ; 3 turns for the 1st archer, 2 more for the second and a final 3 for the last one)
That's all I'm going to post here for now, you'll be able to win knowing this.