Don't worry too much about trying to get kills - Alistar's role in a match is to provide support and disruption. You may not get many killing blows, but if you're a decent player, you should have many many assists instead.
If you're worried about losing out on the money that comes with kills, I'd suggest you look into Gold/10 items on Alistar - Philosopher's Stone and Heart of Gold being the better of the 4 for him. (Duplicate items don't stack, but there's nothing stopping you from picking up one of each).
That said, Alistar makes good use of Sheen, which is a cheap way to double your basic attack damage, and gives him mana to boot.
Alistar is a strong support, but for all his CC, he comes with a few weaknesses. He has to go all in when attacking the enemy; Headbutt (range of 650) puts him right onto the enemy champion’s range and Pulverize has a relatively small area of effect. Since Alistar’s only damage is melee, you can punish him when he approaches the AD or support by using ranged attacks/abilities. You can use these traits against him by warding the side bushes of the lane to stop him from getting into range for his Headbutt/Pulverize combo and by forcing him to use his Triumphant Roar by poking his health down. Poking is something Sona excels at, as Hymn of Valor (her Q, range of 700) plus Power Chord (her passive) allows for a surprising amount of damage at relatively low risk. If the bushes are warded, then you know where Alistar is and can keep him away from your AD carry with Q and passive poke.
Since their AD carry was Caitlyn, they have the advantage early game. Winning lanes is Caitlyn’s main strength, while Tristana is a complete monster late game (though she does have a really mean level 2 if she takes her Rocket Jump). Ideally, Tristana wants to get to mid/late game where her strengths shine. Playing near your tower and having thorough ward coverage is the ideal way of getting to late game without feeding the Caitlyn.
With Nocturne being their jungle and Alistar their support, the chance of a tower dive is pretty high. Alistar’s ultimate (Unbreakable Will. 50% damage reduction at rank 1) allows him to tank the tower damage really easily, and Nocturne’s ultimate (Paranoia) allows him to jump right to Sona or Tristana. You can have a better chance of seeing Nocturne’s ultimate coming by warding the tri-brush and near Dragon. Those wards cover the areas where his range covers bottom lane. The best way to avoid tower dives is to avoid Caitlyn’s Piltover Peacemakers (Q), and use Sona’s ultimate (Crescendo) defensively under the tower. By using Sona’s ultimate under the tower, you can quickly turn a gank into killing multiple enemies with the help of the tower.
Tristana and Sona win their lane by playing defensive and only engaging when they have the clear advantage from poking the enemy down. Even if they don’t win lane, if they can avoid feeding kills to the Caitlyn and stay relatively close on creeps slain (CS), then they come into mid/late game stronger.
Best Answer
Alistar cannot headbutt Dragon nor Baron over the wall, for one simple reason. Baron and Dragon are now both immune to Debuffs and Crowd Control effects, so no displacement spell will ever move them.
Alistar might be able to headbutt the double Golems over the thin wall behind them, but I don't think the walls near Wraiths and Wolves are thin enough to do the same with them.