In order of utility:
Pike - the real counter, but it comes rather late
Muskets - way late, but easier to come by if you are gunning Lib.
Your own Phants - If you can't beat em ...
Maces/Prats - work in a pinch
Pults - great vs stacks, sucks if the opponent divides his forces or has enough to suck up lots of collateral damage.
LBs - defending hills and cities CG III (protective normally) can hold its own.
Swords - best of the earlier units if used right. The trick with elephants is that they can't hold territory worth beans. Let them take the city, but have a stack of CR Pults and swords waiting to smash back. Against a human smart enough to bring plenty of axes this is lower (replace with trebs).
Spears - speed bumps, but you can get a reasonably decent exchange rate if you can avoid too much collateral damage.
Xbows - mainly to help against a balanced stack
axes - useful ony against a balanced stack
