Here's a list of songs from performers featured on ESPN's Little League World Series coverage, along with links to the artists’ websites and links for you to download and buy the songs and/or albums:
1985: "Summer Forever" single (iTunes | Amazon)
American Authors: "Best Day of My Life" from the “Oh, What a Life” album. (iTunes | Amazon)
Avril Lavigne: "Here’s To Never Growing Up" from the “Avril Lavigne” album. (iTunes | Amazon)
Friends in Tokyo: "Let's Go Together" single.