I also play Taric a lot, and I usually find that Soraka and Alistar are very annoying.
Soraka's silence hurts Taric very badly. However, establishing bush dominance is critical. Silence him from the bush, and don't let him get close to your adc, or pain will ensue.
Alistar also works well. Taric's stun is relatively short range, so headbutt him away whenever he tries to get close. A w-q harass combo will ruin Taric's early game ability to support his adc.
As for countering Vayne, pick Caitlyn, Ez, or Varus. All three of them have "pass-through" shots that can hit her behind a wall of minions. Take advantage of the fact that she's squishy early game by picking an, ideally, Alistar/Caitlyn combo against Taric/Vayne. They work well together with Caitlyn's snare and Ali's knock-up.