However, consider Hebrews 5:7,8 "Who in the days of his flesh, when he had offered up prayers and supplications with strong crying and tears unto him that was able to save him from death, and was heard in that he feared; Though he were a Son, yet learned he obedience by the things which he suffered;"
The Lord was no stranger to tears. In his successful struggle against the power of sin, his prayers were of such intensity and passion that they were frequently accompanied by tears. Isaiah (53:3) tells us that the suffering Messiah would be "a man of sorrows, and acquainted with grief" and so, to my mind, tears would have been a constant companion during the years of his ministry.
So the real answer is not "once" not "twice" but, in private, frequently although only two instances of public weeping are recorded.