I love Zulu rushing; they're one of my favourite Civs. So, I'm (reluctantly) putting up a few thoughts for interpretation.
Thinking from the point of view of how I go about rushing, my strategy tends to be to churn out Impi warriors one after another, forsaking growth and research and spending everything I get from Barbarians and Villages on more Impi Warriors. So the first 10-20 turns my only city would be investing all resources in picking up Villages and Barbarians and desperately trying to find other Civs before they have researched and implemented Bronze Working.
An Archer Army ends all charge. It's that simple. In a Zulu rush strategy, my worst nightmare is to have spent everything on Impi Warriors and not take more than one city. If I know the enemy has an Archer Army, then the next thing to try and do is contain that enemy by strangling their city (placing my Impi Warriors in each land tile around the city to stop resources being available) until a later time when I can beat the Archers.
I haven't really thought about how I would counter this, but from experience and from my own opinions, here are some Civs you could look to use (in no particular order):
1) Greeks: Democracy, Courthouse & Hoplites should prove a good counter, with the 50% research/gold bonus under a Democracy you should be able to leap ahead on the Tech front, Courthouse makes the aforementioned strangling difficult (though not impossible
) and Hoplites speak for themselves.
2) English: Longbow defence plus Monarchy culture bonus can provide a solid foundation to build on with a view to getting Knights as early as possible and taking the fight to the Zulu. Culture expands borders for a slightly earlier warning.
3) French: Cathedral culture bonus and Pottery with a view to Masonry. Although an archer army alone should suffice without City Walls, with City Walls two fortified Archers should prove adequate (one for luck, just in case) and again culture will expand those borders for an earlier warning.
4) Aztecs: units heal after combat victory and 25g, this is a big advantage and I'm surprised it hasn't been mentioned yet. Two fortified archers should suffice early on but go for an army for that extra insurance.
5) Spanish: Navigation, Galleons could prove useful for finding Atlantis, escaping overseas and Naval Support. Though a little sketchy.
6) Japanese: +1 food from sea regions allows research and growth for rushing Bronze Working, +1 Samurai Knight attack for when you want to take the fight to the enemy.
With all the above, if I suspected a Zulu rusher in the midst, I would still look to try and get one maybe two Barbarians/Villages under my belt whilst concentrating on 'rush-proofing' my Capital city.
If youre facing a Zulu rusher, watch out for the Chinese! They start with Writing, which if a Zulu rusher gets their hands on means Spies will come and destroy your City Walls and Fortifications.
Eventually you need to think about expanding (unless you're the ultimate OCC player, in which case you carry on and do your thing) and you ideally need to do it in a place where the Zulu rusher won't be able to find it. If the geography permits it and you've been lucky enough, your Capital may be plugging a bottle-neck on a peninsula (not sure what a peninsula is? Land surrounded by water on three sides. Still not sure? Wikipedia is your friend). Build your city/cities behind it and let your Capital be the best defence. Alternatively, you may need to build an Archer Army to escort the Settlers and protect the new founded city; or you could just escape overseas. (If you are confident using the French and their culture, you could use the city conversion tactic to get ahead for a culture victory.)
Another geography tip: build your cities on hills for a 50% defence bonus, if the resources around make it worthwhile. The opposite is also worth noting: try not to build cities next to hills; it gives the attacker a 50% bonus.
Just remember that if you do try to adopt the above, your objective is not just to survive, but to go on to win! Depending on your playing style and the circumstances you'll need to adapt accordingly. You could always try to beat them at their own game and out-rush them (just had a thought, three or four Zulu rushers in one game, now that would be messy).
Another quick tip: if Barbarians give you a Galley, try sticking your attacking unit on the Galley. A Zulu rusher may leave their Capital empty because they've so many land units moving out of their Capital, they think they'd spot any attacks coming (not by sea though). You might just be able to waltz into an empty Capital straight off the boat, making the rusher look a little silly.
If all else fails, just pray that you start on a large island on your own with lots of Villages and Barbarians!
Good luck, hope this helps