1. Scripture Songs: There are all sorts of varieties out there. Our family enjoys Kids Scene Scripture Songs. You can check out a sample HERE.
2. Cedarmont Kids: The Cedarmont Kids produced all kinds of videos and albums back in the day. Some of it is pure fluff (kids need some fluff!), but it is enjoyable. You can view an example HERE. Google and YouTube yield all sorts of results for those videos.
3. Good old hymns: We made it a goal in our house to make hymn lessons a part of our routine. So, for example, we would actually work on one song, as if it were a lesson, until the kids were comfortable singing it. I’ve talked to other parents that started with the same hymn as us: Holy, Holy, Holy. It’s a beautiful hymn that isn’t too difficult to pick up. Here’s a VIDEO with lyrics. Another one that kids seem to pick up fairly quickly is Turn Your Eyes Upon Jesus. You can see that HERE. Our kids were also able to pick up Trust and Obey fairly early on. You can see that HERE. And, last but not least, my personal favorite to sing with the kids is I Must Tell Jesus. You can see that HERE. I like to play this song on the guitar and my kids would willingly repeat the chorus a hundred times if I let them keep going.
4. Psalms: This is tough because Psalm singing has become so rare in American Evangelicalism. There are, however, some that are still sung fairly widely, such as Psalm 23. My own solution to this has been this: I have used The Book of Psalms for Singing and simply created my own tunes using the guitar to sing along with my family. We have learned several whole psalms in this way. The website linked above allows you to listen to the tunes listed for each Psalm in various Psalters.
Thanks for this!