Having thought more about it, I would say that this man is irrational on three counts:
1) He believes that there are refrigerator-sized diamonds.
2) He believes that there is one buried in his backyard.
3) He believes that finding it will bring meaning and fulfillment to his life.
Now let's suppose that the man finds reasonably strong evidence that refrigerator-sized diamonds exist and that one probably is buried in his backyard. Would I consider such a man to be rational? No. Because he still believes that finding it will bring meaning and fulfillment to his life. To believe such a thing is to reveal that you are really sub-human. There is something about you that falls below what it means to be a human being.
To admit that one needs to believe in God in order to have meaning in one's life is saying that existence must ultimately be good and beautiful and the end of all our desires. Such an admission is not irrational, but the proclamation that we are more than just machines, or accidental evolutionary products struggling for survival. We are beings made for something much greater than ourselves.