When my older boys (twins) were approaching 6 years old, I looked hard at what I felt were all of the compound options. They'd had various Walmart type bows they tried to shoot since about 3, but at 5 really started showing more interest.
I ended up getting them diamond prisms thinking they would last through growth spurt a little longer than the atomic but still offer a real shooting solution at their (then) age. They will turn 9 next week and shoot those bows almost daily with me and regularly compete in local 3d shoots with them and 4h shooting sports. I've replaced strings and cables for them this past winter and slowly upgraded a few components here and there over the last few years, but those bows shoot well and are very adjustable. One of my twins is the size of a buddy's 13 year old and his twin brother is about 25 lbs lighter and at least 6" shorter.
This past winter their younger brother (6) was ready to move up from the Walmart type bows and we got him a Mission Radik. It is an awesome little bow that offers a lot but is more expensive compared to the diamonds as it does not come with components. We had extra components (whisker biscuit, sight, etc) laying around as my other boys and wife have upgraded over the years, so those completed his bow.
I would highly recommend either of those bows dependent on budget. Releases, I haven't quite got that dialed in yet with them as they've all been using trufire youth size wrist rockets with varying degrees of success. My twins are getting thumb button next week for their birthday, but I suspect a tension release of some kind might be best to teach the proper principles.
More than anything, just let them have fun. My kids love to set up a couple targets in the yard and just fling arrow after arrow for hours. We pick up lost, broken, etc arrows at local ranges and cut them down, install new inersts if needed ( or cut from the fletched end), and re Fletch with vanes in their favorite colors. My boys enjoy the whole process.
Good luck, and let us know which route you go.