As someone who plays Ali as my main jungler, I can say that the recent nerf to his passive was huge to his early game. He takes much longer to clear the golem so he needs a stronger leash or more time. He is much slower at clearing wraiths/wolves. It's not even worth it for him to try killing small golems.
Early Alistar ganks are best dealt with by your own jungler. Ideally you have a fast jungler who can just intercept him and kill him 1v1 while he's trying to get into position. The alternative is to just gank before him, even if your jungler isn't such a strong ganker. Let's say you have Lee or Shyv. Ali will start blue, you start red. You will finish red before he finishes blue. Immediately go for a gank into mid or the closest end lane. You probably won't get the kill, but you'll either pull Alistar to help the lane or you'll provide protection from the Ali gank. As a result, only one of your lanes has to be careful (the one close to their blue that you didn't gank.)
Ali is great at diving at 6, but if your jungle is playing well, Ali should be hitting 6 at around the time your jungler is hitting 8. Take advantage of that. Ward wraiths and steal them every time. Camp mid so their mid can't take the wraiths or help Ali take them. Steal his red if you can. The best way to do this is to send mid lane or support to help your jungler. If you successfully deny him red (obviously don't let him take your blue, and your red is already taken care of) he will be even more behind. He can't do small golems at any normal speed, so he will have to rely on wolves only to get him from 3 to 6. That will take a very long time
One final thought: In team fights against Alistar it helps a lot if your team has a disengage. I use Janna as a counter to Ali, and it works great. Fight until he ultis, disengage. Now Ali is guaranteed to die if he tries to fight, and you're much better at disabling the team than he is.
Riot has tried to balance gank strength with clear speed. On most junglers, it's at a reasonable place, but Alistar's gank strength is so great that he'd have to lose all clear speed (no passive damage at all, reduced base armor) to be balanced with his gank strength. I expect that there will be nerfs to his ganks coming in the future. The best place to hit is his W. Make it a skillshot which hits first enemy (not always champion) and moves Alistar even if he misses. Alternately, his Q loses the knockup and just becomes a 1 sec aoe stun, like Riven's W.