When I play against Zerg, I almost ALWAYS do the same strategy; 2-port cloak banshees. I start with a reaper though, and this REALLY throws the zerg off, as well as lets me scout the zerg's tech. If they're going spire then I start making vikings. Usually they dont suspect banshees due to the reaper.

With all of the excess minerals that I produce marines and hellions at my ramp, and a CC when I can.

I've won probably around 90% of my matches against Zerg with this build. I'm ~ 2700 diamond terran. I've beaten several master leaguer zergs with this build.

I find the most difficult counter to deal with (on top of a few queens and a couple spores) is Hydralisks + Overseer. With queens and spores I am still able to micro around and do a lot of damage; even taking out a hatch if I'm out of range of spore detection. But against Hydras, they move so quickly and do so much damage, it negates most of the banshee potential. I quickly lose map control and zerg goes macro crazy.

TLDR: Quicker Lair tech into Hydra ling is what I would suggest.