I routinely added lap infants via Twitter (direct message) with Delta, Alaska, and American. By far the easiest. Was typically a one-sentence direct message: "Please add lap infant John Jason Smith (DOB: Jan 1, 2018) to PNR ABCDEF with paid passenger Rebecca Johnson". They'd reply within 2-30 minutes, typically.

(This was in 2014-2016; no more lap infants for me now.)