If nothing on this list suited your fancy, maybe action games aren't the way to go. These are the games I tend to play with my nieces and nephews, but there are a few family friendly genres that may work better for you.
For example, there are some good PS4 games for kids in the sports genre. They've got football, baseball, soccer and basketball games.
Do your kids have the need for speed? Maybe you should get them... Need for Speed. See what I did there?
Puzzle games may be another way to go. Brothers -- A Tale of Two Sons, The Road Not Taken or Perfect Universe are other kid-friendly PS4 games to look into.
Good luck, and don't forget to play these games with your kids! I know I always appreciated it when my Dad took time to play with me, and it's some of the only bonding time I really get with my nieces and nephews.