What's a TMS1232? I can't find it.
Make sure you're not picking up 50/60 Hz line noise, and that your voltage reference isn't noisy. 19 bits it thin air.
If you can't reduce the sample rate, all you could do is add some analog filtering ahead of the ADC, but that equivalently slows it down, so you can't filter too hard.
Is this a weighing application? If so, vibration will be a serious problem, and the only fix is lower sampling rates or more averaging, which amounts to pretty much the same thing.
John