A few years ago, I found out about Noisetrade and I've gone there ever since. Noisetrade tells you they've got "Thousands of Albums. Completely Free. Completely Legal." And they do.
How do they pull this off? By successfully engineering a win-win-win-win for all involved. Artists allow free downloads on Noisetrade to increase publicity for their music (Win). If the downloader wants to leave a tip, they can choose the amount (Win) or they can get it for free (Win). Noisetrade sells advertisements to musicians on their heavily trafficked site (eh hem, Win).
Though the site is open to many different types of musicians, you'll find plenty of Christian ones use the platform. Artists as well known as Jars of Clay and Michael W. Smith are alongside the more obscure.
I visited the site recently and found a kid's sing-a-long album taken from stories and passages of Scripture. I thought you might like some fun, catchy, and free Bible story songs to sing with your kids so here's the link to get them.