Bathtub Drain Stopper too large?
You also find drain assemblies with 1-1/4" tailpieces, but they're almost exclusively used for sinks. They're used with a 1-1/2" to 1-1-/4" reducer since the PVC drain plumbing usually won't be smaller than 1-1/2". 

The diameter of the actual threaded drain assembly isn't smaller in these cases. They fit the sink/tub the same way. Just the tailpiece is smaller. 

Post photos of your situation for more specific advice.