Sadly, there's no sure-fire way of resolving this situation.
You won't be able to rely on minions to take out their towers and nexus, especially if their uber status gets to the point where they can start defending their respawning inhibitors. If you get really lucky and get their nexus towers down, you could just farm minions hard enough for yours to take the nexus down a bit then try to dive the nexus. I'd consider this a Hail Mary more than anything else, though.
If you know you're going up against a team that is going to steamroll you once they get maxxed out (2+ carries), the main goal is to take advantage of the fact that they will be weaker in the early game. If you zone the carries and/or kill them enough to keep them from getting geared and leveled, your team will get powerful enough to take their nexus before they can do anything about it.
Assuming you find yourself in that unfortunate position anyway and forcing their team to split up isn't working, you absolutely have to focus the primary damage dealers down first. If they stick together and you're not killing their carries first, you'll take way more damage than you will deal out over the course of the fight and you're sure to lose.
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
Proxy Singed is a strategy designed to take advantage of Singed strengths and confuse the enemy team.
The strategy is usually executed as following :
The key benefits of the strategy are these :
This strategy is best run with Singed, because he has great escape capabilities with his ult, poison, and ghost. He can farm minion waves easily with his poison while avoiding most of minion damage. Even if Singed dies a lot, he should still get more than decent farms (he can even go farm top and mid lanes inside enemy base after level 6) and be efficient for end game teamfights.
The biggest disadvantage of this strategy is that Proxy Singed requires a team knowing how to take advantage of the map pressure created by Singed. If your teammates don't get objectives while Singed is being chased, the strategy is a lot less efficient.
There is no real hard counter to the strategy, as the enemy team cannot leave Singed farming freely inside their base, but chasing him will leave objectives open. The best ways to handle a proxy farming Singed are :
Note that the latest patch have made the proxy farming less efficient, by reducing the death strike penalty on kills, making killing Singed more rewarding in such cases.