How to get over a fear of pitching in a little ...

I coached a kid who was a great hitter, but was afraid of getting hit.  I had our regular batting practice pitcher pitch to him using tennis balls, and deliberately throw a "beaner" or a "brushback" every so often.  After he got hit by the tennis ball several times, he stopped flinching away from inside ptiches.  Maybe you could get your pitcher to pitch for a week or so at about half speed, using tennis balls, and tell him to deliberatel hit the batter about once every four to six pitches.  I bet the rest of the team would like the extra batting practice, and it could help your pitcher, too.  I think it might be worth a try, anyway.  Best of luck.

Have him throw the ball to someone only a short distance away. As his confidence level increases. Increase the distance of throw until he reaches the proper distance.

That or you could point a gun at his dogs head. ( No. just kidding ) Really )

I'm going under the assumption his control is not that great yet. Have him throw to a target you place on the backstop. Start at a shorter distance and work up to the actual LL distance. Once he's confident with his accuracy he'll be ok. This may take a few weeks. Also talk to him and let him know it's part of the game, it happens all the time and serious injuries are very rare. From a former LL, HS and college player.