In the Gospel of Matthew chapter sixteen we see Jesus asking his disciples "Whom do you say I am?" and Cephas answered, "Thou art the Christ the Son of the Living God."
Jesus replied, "Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven."
This, I think, is an example of Christ's sensitivity to the occasion to fun and the occasion to seriousness, for John 1:42 tells us Jesus had given Simon the nickname Petros, or Rocky. This may well have been Jesus's playful way of telling Simon that He sees right through him, that he knows he is unstable, that is, not exactly a rock when confronted with difficult situations.
Yet here in a serious moment we hear Christ address Cephas as Simon Barjona, that is, Simon Son of Jona, a complete and formal designation of his identity.
Later in the passage we find that when Peter chastises Jesus for his foretelling of his own death, Jesus says, "Get thee behind me, Satan." Here, in fine sarcasm, Jesus rebukes Peter, calling him Satan, not in a literal sense, but metaphorically pointing out that to deny the ultimate sacrifice He was to make is a ploy of Satan, and one that Satan uses to this day.
Jesus was witty, funny, and used biting humor to make his points. Above all things he was sensitive to the moment and appropriate to the occasion, always loving and forgiving to those who accept his love and forgiveness.
Given what I believe about Jesus the Christ it would be impossible for me to think that he had no sense of humor, for while I believe he was fully God, I also believe he was fully human, and a human who was endowed with a sense of humor. Humorless people do not relate well to others, for they lack a sense of nuance in personal interchanges. More, I suspect such people may lean toward sociopathy. I am not a psychologist.