I enthusiastically recommend Dr. Ari Kupietzky located in the Rechavia
neighborhood of Jerusalem. We have been going to him for 2 years, and
my kids LOVE him. He is really amazing and patient. He demonstrates
all procedures first (on himself or the child's hand or on the parent).
My 3-year-old daughter has never cried or been afraid of him since her
first visit at age 18 months.
Here is a little weblink about him.
Best of luck!