Lunch Money is a band based in South Carolina. They play lo-fi children's rock and the songs of theirs I've heard create moments of ear-to-ear grins. So do other things, I suppose, but most of those are the result of family joy and not necessarily from children's music.
Their song "Tricycle" creates a lot of grins for me. It's a very simple song, musically -- guitar, drums, and a surfeit of handclaps. It matches an eminently hummable tune with words that have meaning to both the 3-year-old and their 33-year-old parents. "This tricycle was my brother’s tricycle / and that’s why it has this dent in the fender." It's a goofy little song, but it's sooooo much fun.
Listen to three songs off their first album Silly Reflection here.
For another song with handclaps from a band with an occasionally lo-fi aesthetic, listen to the Shins' "Kissing the Lipless" here.
(Hat tip to Bill from Spare the Rock, Spoil the Child for the Lunch Money advocacy.)