First, make sure that all of the players hats and equipment have their names on them. This is a tip I would like to share that will assist you thru out the season when players lose their hats, gloves, bats or any other piece of equipment. The very first thing I do when I hand out hats and uniforms at the start of the season is to make sure that each child's name is written on the inside portion of the bill of their baseball caps. While we are at it I have the parents write the child's name on their baseball mitts and baseball bats. If you are a coach you know what happens after each and every game or practice, left behind equipment. This is a great way to make sure the rightful owner gets their equipment back in short order so they can use it to practice with at home.
Once the hats have been labeled with the players name or uniform number you are ready to construct a fun and impartial line up and batting order.
Gather all of the players hats into a pile. The way I do it I have all of the players take their hats off and hand it to one of the players or coaches. Remember, each of these hats has a child's name written on the inside of the bill.
Next, I have each player take a turn picking a hat out of the pile. Whatever name is on it bats first. Then another player picks another hat, the name on that hat now gets to bat second....and so on. We do this before each Tee Ball game we play.
This makes the line up totally random and the kids actually have fun doing it. The parents also like the idea that their child will have the opportunity to bat first if they have their hat pulled.
Everyone is happy with this method and it has worked great for me for many years!