HihihiBottom with Ezreal
But seriously the deal with taric is just being annoying as fuck, land a stun if the enemy gets out of position and just start whaling on him. Remember that your auto atks means more mana and shorter heal cooldowns and dont expect your carry to be the one initiating. Basically, make shit happen.
In team fights you're supposed to be "suicidal". You get in there and stun the carry so your team can take him out, try to land your r+w combo if they're all together but if not just use r even if it doesn't hit anything. After that just really get in there, again your attacks mean more heals and mana. In general they won't be wanting to focus you, if they're dumb enough to do that just use your heals on yourself and don't use w for the armor. Plus, don't forget to use your items.
Honestly, supporting with Taric is easy as fuck. No hard to land skillshots, you don't have to worry about positioning nearly as much as other squishy healers all of your spells are useful 90% of the time in one way or another.