First of all you have to protect your cities of course. This can be achieved by building them on hills. Also hunters with anti horse promo on hills will make sure those cities won't be taken easily. Noobs who are about building their third city at turn 55 and defending the other two with 2 warriors will of course die to the rush.
m2m got a nice idea there too. Allthough I doubt you could do this in every direction and have enough forces to defend your city (as long as you dont play on noble and the rusher play on emperor) while the centaurs are free to circle behind your city and attack from there if the terrain is not stopping them from it.
Improvements will be pillaged though and this really hurts you and puts you at a disadvantage. Maybe you can try to do the same stuff on him, moving a stack of hunters into his borders and pillaging his improvements, forcing him to retreat.
(EDIT: Hunters cant pillage though, you need to add a warrior to the stack )
Of course you should scout your direct neighbour with Birds anyways, so you will be able to see the growing number of centaurs in his city and react while there is plenty of time to do so e.g. building up your own troops and/or rush him before he rushes you.
Unfortunately a rush and even if it is only a pillage-rush will usually hurt the rushed one more then the rusher unless the rusher leads his units into a desaster.
This is all about the Sun Tzu guy and chosing the Battleground ofc.
PS. We finally got a strategy subforum now. So feel free to use it and move your topic over there.
By fire be purged
dynablaster
