Here's a tip to make it easier on your kids.
Have your child practice eye contact any time you go to a restaurant by having him order his own meal. Go over the menu with your child first, have him practice ordering with you and then, when the server approaches, let your child try it. Reassure your child beforehand that you are there should he stumble. It may be a bit of a struggle at first, but with practice, I'm quite certain, it will get easier.
Don't get out to restaurants much? I get it -- I have 4 little kids myself. Instead, try asking your child to say hello to the grocery store clerk, an acquaintance at church, or even practice making eye contact with her teacher at school. You can use hand or finger puppets at home to go over different dialogues and possible conversations. Good luck!